Repeat-Free Schedule Coverage

version 1 · visual region g=1..10, p=1..10 · benchmark regions Canonical benchmark region g=2..10, p=2..10 · Canonical benchmark region g=11..20, p=2..10 · Canonical benchmark region g=11..20, p=11..20 · Canonical benchmark region g=21..30, p=1..10 · Canonical benchmark region g=21..30, p=11..20 · Canonical benchmark region g=21..30, p=21..30 · Canonical benchmark region g=31..40, p=1..10

Fillfar from targetclose to targettarget reachedvisual-only

Borderoptimum reachedoptimum known, not reachedoptimum unknown

Corners, same in all matrices O top-left proven optimum when known ✓ top-left counting upper bound reached when no stronger optimum is encoded T top-right curated target/literature target U bottom-left counting upper bound tiny blue superscripts on T labels link into the literature reference table below when a source is curated

Method badges RR round robin NKTS nearly Kirkman triple system MOLR Latin-rectangle lower bound from explicit MOLS ownSG starter-block own-social-golfer construction RITD resolvable incomplete transversal design PSB published schedule bank

Fill denominator fill is progress to T when a target is present; otherwise progress to U

Solved and optimal

✓

U19

green border/✓ means the counting upper bound or encoded optimum is reached

Below target

T10

U13

RTD

T and U keep the same corner meanings everywhere

Literature and optimum ahead

O11

T10

U13

PSB→RBIBD

O shows a proven optimum; method arrows show an implemented family below a desired family

No implementation yet

empty-looking cells stay quiet; the fill already tells the story

Coverage dashboard

g\p	1	2	3	4	5	6	7	8	9	10
1	v T∞ ∞	v T1 1	v T1 1	v T1 1	v T1 1	v T1 1	v T1 1	v T1 1	v T1 1	v T1 1
2	v T∞ ∞	O3 T3¹ U3 3 RR	O1 T1¹ U1 1 NKTS	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W
3	v T∞ ∞	O5 T5¹ U5 5 RR	O4 T4¹ U4 4 KTS	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W
4	v T∞ ∞	O7 T7¹ U7 7 RR	O4 T4¹ U5 4 RTD	O5 T5¹ U5 5 AP	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W
5	v T∞ ∞	O9 T9¹ U9 9 RR	O7 T7¹ U7 7 KTS	O5 T5¹ U6 5 RTD	O6 T6¹ U6 6 AP	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W
6	v T∞ ∞	O11 T11¹ U11 11 RR	O8 T8¹ U8 8 NKTS	O7 T7¹ U7 7 RGDD4	T6¹ U7 6 PSB	O3 T1¹ U7 3 MOLR+G	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W
7	v T∞ ∞	O13 T13¹ U13 13 RR	O10 T10¹ U10 10 KTS(6t+3)	O9 T9¹ U9 9 RGDD4	T7¹ U8 7 RTD	T7¹ U8 7 RTD	O8 T8¹ U8 8 AP	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W
8	v T∞ ∞	O15 T15¹ U15 15 RR	O11 T11¹ U11 11 NKTS	O10 T10¹ U10 10 RGDD4	T8¹ U9 8 RTD	T8¹ U9 8 RTD	T8¹ U9 8 RTD	O9 T9¹ U9 9 AP	O1 T1¹ U1 1 1W	O1 T1¹ U1 1 1W
9	v T∞ ∞	O17 T17¹ U17 17 RR	O13 T13¹ U13 13 KTS	O11 T11¹ U11 11 RGDD4	T9¹ U11 9 RTD	T9¹ U10 9 RTD	T9¹ U10 9 RTD	T9¹ U10 9 RTD	O10 T10¹ U10 10 AP	O1 T1¹ U1 1 1W
10	v T∞ ∞	O19 T19¹ U19 19 RR	O14 T14¹ U14 14 NKTS	O13 T13¹ U13 13 RGDD4	T9¹ U12 9 RITD	T7¹ U11 9 DM+K	T7¹ U11 8 DM	T5¹ U11 9 DM+K	T5¹ U11 5 ownSG	T4¹ U11 4 MOLR+G

Canonical coverage: g=11..20, p=1..10

Canonical benchmark region. Center = current constructed weeks, top-right = conservative literature target T when curated from the 2026 paper, bottom-left = counting upper bound U when a curated target exists, and bottom-right = achieving family. Fill grades against T when present, otherwise against U. Only the trivial p=1 column is visual-only.

g\p	1	2	3	4	5	6	7	8	9	10
11	v ∞	✓ T21¹ U21 21 RR	✓ T16¹ U16 16 KTS	✓ T14¹ U14 14 RGDD4	T11¹ U13 11 RTD	T11¹ U13 11 RTD	T11¹ U12 11 RTD	T11¹ U12 11 RTD	✓ T12¹ U12 12 RGDD	T11¹ U12 11 RTD
12	v ∞	✓ T23¹ U23 23 RR	✓ T17¹ U17 17 NKTS	✓ T15¹ U15 15 RGDD4	T12¹ U14 12 MOLS	T13¹ U14 13 MOLS+G	T7¹ U13 9 DM	T6¹ U13 9 DM	T6¹ U13 7 DM	T6¹ U13 6 MOLR
13	v ∞	✓ T25¹ U25 25 RR	✓ T19¹ U19 19 KTS(6t+3)	✓ T17¹ U17 17 RGDD4	✓ T16¹ U16 16 RBIBD5	T13¹ U15 13 RTD	T13¹ U15 13 RTD	T13¹ U14 13 RTD	T13¹ U14 13 RTD	T13¹ U14 13 RTD
14	v ∞	✓ T27¹ U27 27 RR	✓ T20¹ U20 20 NKTS	✓ T18¹ U18 18 RGDD4	T14¹ U17 14 MOLS	T9¹ U16 11 DM	T9¹ U16 11 DM+K	T8¹ U15 9 DM	T7¹ U15 7 ownSG	T5¹ U15 6 DM
15	v ∞	✓ T29¹ U29 29 RR	✓ T22¹ U22 22 KTS	✓ T19¹ U19 19 RGDD4	T16¹ U18 16 MOLS+G	T10¹ U17 12 DM	T5¹ U17 10 DM	✓ T17¹ U17 17 RBIBD	T7¹ U16 8 DM	T5¹ U16 7 DM
16	v ∞	✓ T31¹ U31 31 RR	✓ T23¹ U23 23 NKTS	✓ T21¹ U21 21 RGDD4	T16¹ U19 16 RTD	T16¹ U19 16 RTD	T16¹ U18 16 RTD	T17¹ U18 17 RTD+G	T16¹ U17 16 RTD	T16¹ U17 16 RTD
17	v ∞	✓ T33¹ U33 33 RR	✓ T25¹ U25 25 KTS	✓ T22¹ U22 22 RGDD4	✓ T21¹ U21 21 RBIBD5	T17¹ U20 17 RTD	T17¹ U19 17 RTD	T17¹ U19 17 RTD	T17¹ U19 17 RTD	T17¹ U18 17 RTD
18	v ∞	✓ T35¹ U35 35 RR	✓ T26¹ U26 26 MOLS+G	✓ T23¹ U23 23 RGDD4	T18¹ U22 18 MOLS	T19¹ U21 19 MOLS+G	T10¹ U20 13 DM	T6¹ U20 11 DM	T6¹ U20 10 DM	T6¹ U19 9 DM
19	v ∞	✓ T37¹ U37 37 RR	✓ T28¹ U28 28 KTS(6t+3)	✓ T25¹ U25 25 RGDD4	T19¹ U23 19 RTD	T19¹ U22 19 RTD	T19¹ U22 19 RTD	T19¹ U21 19 RTD	T19¹ U21 19 RTD	T19¹ U21 19 RTD
20	v ∞	✓ T39¹ U39 39 RR	✓ T29¹ U29 29 NKTS	✓ T26¹ U26 26 RGDD4	T21¹ U24 21 RTD-QDM+G	T13¹ U23 16 DM	T5¹ U23 15 DM	T5¹ U22 13 DM	T5¹ U22 12 DM	T5¹ U22 10 DM

Canonical coverage: g=11..20, p=11..20

Canonical diagonal/high-p benchmark region. Center = current constructed weeks, top-right = conservative literature target T when curated from the 2026 paper, bottom-left = counting upper bound U when a curated target exists, and bottom-right = achieving family. Fill grades against T when present, otherwise against U. Blank T means no clean paper-derived target is curated yet for that cell, but the cell still counts in the benchmark via its current constructed weeks and counting upper bound.

g\p	11	12	13	14	15	16	17	18	19	20
11	✓ T12¹ U12 12 AP	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
12	T6¹ U13 6 MOLR	T7¹ U13 7 MOLR+G	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
13	T13¹ U14 13 RTD	T13¹ U14 13 RTD	✓ T14¹ U14 14 AP	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
14	T5¹ U15 6 DM	T5¹ U15 5 MOLR	T5¹ U15 6 ?	T5¹ U15 6 MOLR+G	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
15	T5¹ U16 7 DM	T5¹ U16 5 MOLR	T5¹ U16 5 MOLR	T5¹ U16 5 MOLR	T5¹ U16 6 MOLR+G	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
16	T16¹ U17 16 RTD	T16¹ U17 16 RTD	T16¹ U17 16 RTD	T16¹ U17 16 RTD	T16¹ U17 16 RTD	✓ T17¹ U17 17 AP	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
17	T17¹ U18 17 RTD	T17¹ U18 17 RTD	T17¹ U18 17 RTD	T17¹ U18 17 RTD	T17¹ U18 17 RTD	T17¹ U18 17 RTD	✓ T18¹ U18 18 AP	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
18	T6¹ U19 8 DM	T6¹ U19 7 DM	T6¹ U19 6 MOLR	T6¹ U19 6 MOLR	T6¹ U19 6 MOLR	T6¹ U19 6 MOLR	T6¹ U19 6 MOLR	T6¹ U19 7 MOLR+G	✓ U1 1 1W	✓ U1 1 1W
19	T19¹ U20 19 RTD	T19¹ U20 19 RTD	T19¹ U20 19 RTD	T19¹ U20 19 RTD	T19¹ U20 19 RTD	T19¹ U20 19 RTD	T19¹ U20 19 RTD	T19¹ U20 19 RTD	✓ T20¹ U20 20 AP	✓ U1 1 1W
20	T5¹ U21 9 DM	T5¹ U21 8 DM	T5¹ U21 7 DM	T5¹ U21 7 DM	T5¹ U21 6 DM	T5¹ U21 6 DM	T5¹ U21 5 MOLR	T5¹ U21 5 MOLR	T5¹ U21 5 MOLR	T5¹ U21 6 MOLR+G

Canonical coverage: g=21..30, p=1..10

Canonical benchmark region. Center = current constructed weeks, top-right = conservative literature target T when curated from the 2026 paper, bottom-left = counting upper bound U, and bottom-right = achieving family. Fill grades against T when present, otherwise against U. Only the trivial p=1 column is visual-only.

g\p	1	2	3	4	5	6	7	8	9	10
21	v ∞	✓ T41¹ U41 41 RR	✓ T31¹ U31 31 KTS	✓ T27¹ U27 27 RGDD4	✓ T26¹ U26 26 RBIBD5	✓ T25¹ U25 25 RBIBD	T7¹ U24 16 DM+K	T6¹ U23 13 DM	T6¹ U23 12 DM	T6¹ U23 11 DM
22	v ∞	✓ T43¹ U43 43 RR	✓ T32¹ U32 32 NKTS	✓ T29¹ U29 29 RGDD4	T19¹ U27 20 DM	T14¹ U26 18 DM	T4¹ U25 16 DM	T4¹ U25 15 DM+K	T4¹ U24 13 DM	T4¹ U24 12 DM
23	v ∞	✓ T45¹ U45 45 RR	✓ T34¹ U34 34 KTS	T29¹ U30 29 URD	T23¹ U28 23 RTD	T23¹ U27 23 RTD	T23¹ U26 23 RTD	T23¹ U26 23 RTD	T23¹ U25 23 RTD	T23¹ U25 23 RTD
24	v ∞	✓ T47¹ U47 47 RR	✓ T35¹ U35 35 MOLS+G	✓ T31¹ U31 31 MOLS+G	✓ T29¹ U29 29 RGDD	T25¹ U28 25 MOLS+G	T24¹ U27 24 MOLS	T24¹ U27 25 MOLS+G	T8¹ U26 14 DM	T8¹ U26 13 DM
25	v ∞	✓ T49¹ U49 49 RR	✓ T37¹ U37 37 KTS(6t+3)	✓ T33¹ U33 33 DMA	✓ T31¹ U31 31 AG	T25¹ U29 25 RTD	T25¹ U29 25 RTD	T25¹ U28 25 RTD	T25¹ U28 25 RTD	T25¹ U27 25 RTD
26	v ∞	✓ T51¹ U51 51 RR	✓ T38¹ U38 38 NKTS	✓ T34¹ U34 34 RGDD4	T26¹ U32 26 MOLS	✓ T15¹ U31 31 RBIBD	T5¹ U30 20 DM+K	T5¹ U29 17 DM	T5¹ U29 17 DM+K	T5¹ U28 14 DM
27	v ∞	✓ T53¹ U53 53 RR	✓ T40¹ U40 40 KTS	✓ T35¹ U35 35 RGDD4	T27¹ U33 27 RTD	T27¹ U32 27 RTD	T27¹ U31 27 RTD	T27¹ U30 27 RTD	T27¹ U30 28 RTD+G	T27¹ U29 27 RTD
28	v ∞	✓ T55¹ U55 55 RR	✓ T41¹ U41 41 NKTS	✓ T37¹ U37 37 MOLS+G	T28¹ U34 28 MOLS	T28¹ U33 28 MOLS	T6¹ U32 20 DM	T6¹ U31 19 DM+K	T6¹ U31 17 DM	T6¹ U31 15 DM
29	v ∞	✓ T57¹ U57 57 RR	✓ T43¹ U43 43 KTS	✓ T38¹ U38 38 RGDD4	✓ T36¹ U36 36 RBIBD5	T29¹ U34 29 RTD	T29¹ U33 29 RTD	✓ T29¹ U33 33 DMA	T29¹ U32 29 RTD	T29¹ U32 29 RTD
30	v ∞	✓ T59¹ U59 59 RR	✓ T44¹ U44 44 NKTS	✓ T39¹ U39 39 RGDD4	T36¹ U37 36 MOLS+G	T5¹ U35 25 DM+K	T5¹ U34 22 DM	T5¹ U34 20 DM+K	T5¹ U33 18 DM	T5¹ U33 16 DM

Canonical coverage: g=21..30, p=11..20

g\p	11	12	13	14	15	16	17	18	19	20
21	T6¹ U23 10 DM	T6¹ U22 8 DM	T6¹ U22 8 DM	T6¹ U22 6 MOLR	T6¹ U22 6 MOLR	T6¹ U22 6 MOLR	T6¹ U22 6 MOLR	T6¹ U22 6 MOLR	T6¹ U22 6 MOLR	T6¹ U22 6 MOLR
22	T4¹ U24 10 DM	T4¹ U23 9 DM	T4¹ U23 8 DM	T4¹ U23 7 DM	T4¹ U23 6 DM	T4¹ U23 5 DM	T4¹ U23 5 DM	T4¹ U23 4 MOLR	T4¹ U23 4 MOLR	T4¹ U23 4 MOLR
23	T23¹ U25 23 RTD	T23¹ U25 23 RTD	T23¹ U24 23 RTD	T23¹ U24 23 RTD	T23¹ U24 23 RTD	T23¹ U24 23 RTD	T23¹ U24 23 RTD	T23¹ U24 23 RTD	T23¹ U24 23 RTD	T23¹ U24 23 RTD
24	T8¹ U26 12 DM	T8¹ U26 10 DM	T8¹ U25 9 DM	T8¹ U25 8 MOLR	T8¹ U25 8 MOLR	T8¹ U25 8 MOLR	T8¹ U25 8 MOLR	T8¹ U25 8 MOLR	T8¹ U25 8 MOLR	T8¹ U25 8 MOLR
25	T25¹ U27 25 RTD	T25¹ U27 25 RTD	T25¹ U27 25 RTD	T25¹ U26 25 RTD	T25¹ U26 25 RTD	T25¹ U26 25 RTD	T25¹ U26 25 RTD	T25¹ U26 25 RTD	T25¹ U26 25 RTD	T25¹ U26 25 RTD
26	T5¹ U28 13 DM	T5¹ U28 12 DM	T5¹ U28 9 DM	T5¹ U27 8 DM	T5¹ U27 7 DM	T5¹ U27 6 DM	T5¹ U27 6 DM	T5¹ U27 5 MOLR	T5¹ U27 5 MOLR	T5¹ U27 5 MOLR
27	T27¹ U29 27 RTD	T27¹ U29 27 RTD	T27¹ U29 27 RTD	T27¹ U29 27 RTD	T27¹ U28 27 RTD	T27¹ U28 27 RTD	T27¹ U28 27 RTD	T27¹ U28 27 RTD	T27¹ U28 27 RTD	T27¹ U28 27 RTD
28	T6¹ U30 14 DM	T6¹ U30 13 DM	T6¹ U30 10 DM	T6¹ U30 8 DM	T6¹ U29 8 DM	T6¹ U29 7 DM	T6¹ U29 6 MOLR	T6¹ U29 6 MOLR	T6¹ U29 6 MOLR	T6¹ U29 6 MOLR
29	T29¹ U31 29 RTD	T29¹ U31 29 RTD	T29¹ U31 29 RTD	T29¹ U31 29 RTD	T29¹ U31 29 RTD	T29¹ U30 29 RTD	T29¹ U30 29 RTD	T29¹ U30 29 RTD	T29¹ U30 29 RTD	T29¹ U30 29 RTD
30	T5¹ U32 15 DM	T5¹ U32 14 DM	T5¹ U32 11 DM	T5¹ U32 9 DM	T5¹ U32 8 DM	T5¹ U31 8 DM	T5¹ U31 7 DM	T5¹ U31 6 DM	T5¹ U31 6 DM	T5¹ U31 6 DM

Canonical coverage: g=21..30, p=21..30

Canonical high-p benchmark region. Center = current constructed weeks, top-right = conservative literature target T when curated from the 2026 paper, bottom-left = counting upper bound U when a curated target exists, and bottom-right = achieving family. Fill grades against T when present, otherwise against U. Blank T means no clean paper-derived target is curated yet for that cell, but the cell still counts in the benchmark via its current constructed weeks and counting upper bound.

g\p	21	22	23	24	25	26	27	28	29	30
21	T7¹ U22 7 MOLR+G	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
22	T4¹ U23 4 MOLR	T5¹ U23 5 MOLR+G	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
23	T23¹ U24 23 RTD	T23¹ U24 23 RTD	✓ T24¹ U24 24 AP	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
24	T8¹ U25 8 MOLR	T8¹ U25 8 MOLR	T8¹ U25 8 MOLR	T9¹ U25 9 MOLR+G	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
25	T25¹ U26 25 RTD	T25¹ U26 25 RTD	T25¹ U26 25 RTD	T25¹ U26 25 RTD	✓ T26¹ U26 26 AP	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
26	T5¹ U27 5 MOLR	T5¹ U27 5 MOLR	T5¹ U27 5 MOLR	T5¹ U27 5 MOLR	T5¹ U27 5 MOLR	T6¹ U27 6 MOLR+G	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
27	T27¹ U28 27 RTD	T27¹ U28 27 RTD	T27¹ U28 27 RTD	T27¹ U28 27 RTD	T27¹ U28 27 RTD	T27¹ U28 27 RTD	✓ T28¹ U28 28 AP	✓ U1 1 1W	✓ U1 1 1W	✓ U1 1 1W
28	T6¹ U29 6 MOLR	T6¹ U29 6 MOLR	T6¹ U29 6 MOLR	T6¹ U29 6 MOLR	T6¹ U29 6 MOLR	T6¹ U29 6 MOLR	T6¹ U29 6 MOLR	T7¹ U29 7 MOLR+G	✓ U1 1 1W	✓ U1 1 1W
29	T29¹ U30 29 RTD	T29¹ U30 29 RTD	T29¹ U30 29 RTD	T29¹ U30 29 RTD	T29¹ U30 29 RTD	T29¹ U30 29 RTD	T29¹ U30 29 RTD	T29¹ U30 29 RTD	✓ T30¹ U30 30 AP	✓ U1 1 1W
30	T5¹ U31 5 MOLR	T5¹ U31 5 MOLR	T5¹ U31 5 MOLR	T5¹ U31 5 MOLR	T5¹ U31 5 MOLR	T5¹ U31 5 MOLR	T5¹ U31 5 MOLR	T5¹ U31 5 MOLR	T5¹ U31 5 MOLR	T6¹ U31 6 MOLR+G

Canonical coverage: g=31..40, p=1..10

Canonical benchmark region adjacent to the larger group-count region now exercised by adjacent-size design. Center = current constructed weeks, top-right = conservative literature target T when curated, bottom-left = counting upper bound U, and bottom-right = achieving family. Fill grades against T when present, otherwise against U. Only the trivial p=1 column is visual-only.

g\p	1	2	3	4	5	6	7	8	9	10
31	v ∞	✓ T61¹ U61 61 RR	✓ T46¹ U46 46 KTS(6t+3)	✓ T41¹ U41 41 RGDD4	T31¹ U38 31 RTD	✓ T31¹ U37 37 RBIBD	T31¹ U36 31 RTD	T31¹ U35 31 RTD	T31¹ U34 31 RTD	T31¹ U34 31 RTD
32	v ∞	✓ T63¹ U63 63 RR	✓ T47¹ U47 47 NKTS	✓ T42¹ U42 42 RGDD4	T32¹ U39 32 RTD	T32¹ U38 32 RTD	T32¹ U37 32 RTD	T33¹ U36 33 RTD+G	T32¹ U35 32 RTD	T32¹ U35 32 RTD
33	v ∞	✓ T65¹ U65 65 RR	✓ T49¹ U49 49 KTS	✓ T43¹ U43 43 RGDD4	✓ T33¹ U41 41 RBIBD5	T33¹ U39 33 MOLS	T6¹ U38 25 DM+K	T6¹ U37 22 DM+K	T6¹ U37 20 DM	T6¹ U36 18 DM
34	v ∞	✓ T67¹ U67 67 RR	✓ T50¹ U50 50 NKTS	✓ T45¹ U45 45 RGDD4	T34¹ U42 34 MOLS	T5¹ U40 28 DM+K	T5¹ U39 25 DM+K	T5¹ U38 23 DM+K	T5¹ U38 21 DM+K	T5¹ U37 19 DM
35	v ∞	✓ T69¹ U69 69 RR	✓ T52¹ U52 52 KTS	T45¹ U46 45 URD	T42¹ U43 42 MOLS+G	T35¹ U41 35 MOLS	T36¹ U40 36 MOLS+G	T5¹ U39 24 DM+K	T5¹ U39 22 DM+K	T5¹ U38 20 DM
36	v ∞	✓ T71¹ U71 71 RR	✓ T53¹ U53 53 MOLS+G	✓ T47¹ U47 47 MOLS+G	T36¹ U44 36 MOLS	T39¹ U43 39 MOLS+G	T36¹ U41 36 MOLS	✓ T36¹ U41 41 RBIBD	T37¹ U40 37 MOLS+G	T9¹ U39 19 DM
37	v ∞	✓ T73¹ U73 73 RR	✓ T55¹ U55 55 KTS(6t+3)	✓ T49¹ U49 49 RGDD4	✓ T37¹ U46 46 RBIBD5	T37¹ U44 37 RTD	T37¹ U43 37 RTD	T37¹ U42 37 RTD	T37¹ U41 37 RTD	T37¹ U41 37 RTD
38	v ∞	✓ T75¹ U75 75 RR	✓ T56¹ U56 56 NKTS	✓ T50¹ U50 50 RGDD4	T38¹ U47 38 MOLS	T2¹ U45 31 DM+K	T2¹ U44 28 DM+K	T2¹ U43 25 DM+K	T2¹ U42 24 DM+K	T2¹ U42 21 DM
39	v ∞	✓ T77¹ U77 77 RR	✓ T58¹ U58 58 KTS	✓ T51¹ U51 51 RGDD4	T39¹ U48 39 MOLS	T39¹ U46 39 MOLS	T3¹ U45 29 DM+K	T3¹ U44 26 DM+K	T3¹ U43 24 DM+K	T3¹ U43 21 DM
40	v ∞	✓ T79¹ U79 79 RR	✓ T59¹ U59 59 NKTS	✓ T53¹ U53 53 MOLS+G	T48¹ U49 48 MOLS+G	T40¹ U47 40 MOLS	T40¹ U46 40 MOLS	T41¹ U45 41 MOLS+G	T5¹ U44 25 DM+K	T6¹ U44 22 DM

Canonical coverage: g=41..50, p=1..10

Canonical benchmark region extending the larger group-count coverage. Center = current constructed weeks, top-right = conservative literature target T when curated, bottom-left = counting upper bound U, and bottom-right = achieving family. Fill grades against T when present, otherwise against U. Only the trivial p=1 column is visual-only.

g\p	1	2	3	4	5	6	7	8	9	10
41	v ∞	✓ T81¹ U81 81 RR	✓ T61¹ U61 61 KTS	T53¹ U54 53 URD	T41¹ U51 41 RTD	T41¹ U49 41 RTD	T41¹ U47 41 RTD	T41¹ U46 41 RTD	T41¹ U46 41 RTD	T41¹ U45 41 RTD
42	v ∞	✓ T83¹ U83 83 RR	✓ T62¹ U62 62 MOLS+G	✓ T55¹ U55 55 RGDD4	T42¹ U52 42 MOLS	T42¹ U50 49 MOLS+G	T6¹ U48 29 DM	T6¹ U47 27 DM	T6¹ U47 26 DM	T6¹ U46 22 DM
43	v ∞	✓ T85¹ U85 85 RR	✓ T64¹ U64 64 KTS(6t+3)	✓ T57¹ U57 57 RGDD4	T43¹ U53 43 RTD	T43¹ U51 43 RTD	T43¹ U50 43 RTD	T43¹ U49 43 RTD	T43¹ U48 43 RTD	T43¹ U47 43 RTD
44	v ∞	✓ T87¹ U87 87 RR	✓ T65¹ U65 65 NKTS	✓ T58¹ U58 58 MOLS+G	T44¹ U54 44 MOLS	T44¹ U52 44 MOLS	T6¹ U51 31 DM	T6¹ U50 29 DM	T6¹ U49 25 DM	T6¹ U48 24 DM
45	v ∞	✓ T89¹ U89 89 RR	✓ T67¹ U67 67 KTS	✓ T59¹ U59 59 RGDD4	T45¹ U56 54 MOLS+G	T45¹ U53 45 MOLS	T45¹ U52 45 MOLS	T7¹ U51 29 DM	T7¹ U50 26 DM	T7¹ U49 24 DM
46	v ∞	✓ T91¹ U91 91 RR	✓ T68¹ U68 68 NKTS	✓ T61¹ U61 61 RGDD4	T46¹ U57 46 MOLS	T5¹ U55 35 DM	T5¹ U53 32 DM	T5¹ U52 29 DM	T5¹ U51 27 DM	T5¹ U51 25 DM
47	v ∞	✓ T93¹ U93 93 RR	✓ T70¹ U70 70 KTS	T61¹ U62 61 URD	T47¹ U58 47 RTD	T47¹ U56 47 RTD	T47¹ U54 47 RTD	T47¹ U53 47 RTD	T47¹ U52 47 RTD	T47¹ U52 47 RTD
48	v ∞	✓ T95¹ U95 95 RR	✓ T71¹ U71 71 RTD-DM+G	✓ T63¹ U63 63 RTD-DM+G	T48¹ U59 48 RTD-DM	T48¹ U57 56 RTD-DM+G	T48¹ U55 48 RTD-DM	T48¹ U54 49 RTD-DM+G	T48¹ U53 48 RTD-DM	T9¹ U53 26 DM
49	v ∞	✓ T97¹ U97 97 RR	✓ T73¹ U73 73 KTS(6t+3)	✓ T65¹ U65 65 DMA	T49¹ U61 49 RTD	T49¹ U58 49 RTD	✓ T49¹ U57 57 RTD+G	T49¹ U55 49 RTD	T49¹ U55 49 RTD	T49¹ U54 49 RTD
50	v ∞	✓ T99¹ U99 99 RR	✓ T74¹ U74 74 NKTS	T65¹ U66 65 URD	T50¹ U62 57 MOLS+G	T50¹ U59 50 MOLS	T50¹ U58 50 MOLS	T7¹ U57 32 DM	T7¹ U56 29 DM	T7¹ U55 26 DM

Method abbreviations

Code	Stands for	Families / cells it can solve
`RR`	round robin / 1-factorization	implemented `p=2` route across the scored matrix
`KTS(6t+3)`	Kirkman triple system on `6t+3` players	implemented `p=3` family on `v = 6t+3` players via the shipped Kirkman constructor
`KTS`	Kirkman triple system	literature/reference `p=3` targets where a Kirkman triple-system route is the intended benchmark
`NKTS`	nearly Kirkman triple system	literature/reference `p=3` composite-row targets that need nearly-Kirkman constructions
`MOLS`	explicit mutually orthogonal Latin squares with a distinguished resolution square	catalog-backed non-prime-power transversal constructions where one explicit Latin square indexes the parallel classes and the remaining squares provide symbol groups
`MOLSx`	direct-product mutually orthogonal Latin squares	composite transversal constructions built from direct products of smaller prime-power MOLS banks, again using one product square as the parallel-class index
`RTD-QDM`	resolvable transversal design from a quasi-difference matrix	catalog-backed non-prime-power RTD constructions built by expanding an explicit quasi-difference matrix into a resolvable orthogonal array and then reading off the parallel classes
`MOLR`	mutually orthogonal Latin rectangles from an explicit MOLS bank	Sharma-Das lower-bound constructions that use the first k rows of an explicit MOLS bank to produce g+1 rounds, with optional extra clique rounds when the unused rows support them
`ownSG`	starter-block own-social-golfer construction	catalog-backed Appendix A starter-block development family; currently covers large `10-p` rows such as `10-6-7`, `10-7-7`, `10-8-5`, and `10-9-5`
`RITD`	resolvable incomplete transversal design	catalog-backed incomplete-transversal route where deleting one source group yields complete parallel classes, optionally followed by an intra-group filler week such as the shipped `10-5-9` construction
`MOLR+G`	MOLR / MOLS lower-bound route with group fill	catalog-backed non-prime-power square-order route that extends a compatible 3-round `10-10` base with one latent-group filler week, matching the shipped `10-10-4` lower bound
`DM`	cyclic partite difference matrix	catalog-backed exact zero-repeat constructions expanded from certified modular difference-matrix artifacts
`DM+K`	difference matrix plus leave-graph clique factor	catalog-backed constructions that expand a cyclic partite difference matrix, then append stored K_group_size-factors from the leave graph
`RBIBD5`	block-size-5 resolvable balanced incomplete block design	validated explicit schedules whose method source is the RBIBD(v,5) spectrum `v ≡ 5 (mod 20)` outside the named exceptions
`RBIBD`	catalog-backed resolvable balanced incomplete block design	explicit source-backed resolvable BIBD cases such as the shipped `RBIBD(120,8,1)` route for `15-8-17`
`DMA`	Denniston maximal arc / resolvable BIBD finite-geometry construction	power-of-two cells `p=2^a`, `s=(g-1)/(p-1)=2^b` via an `RBIBD(qp-q+p,p,1)` from a Denniston maximal arc in `AG(2,q)`; includes `29-8-33`
`PSB`	published schedule bank	explicit source-backed lower-bound schedules that are honest patch-bank constructions rather than general theorem families
`RTD`	resolvable transversal design	implemented prime-power `g-p-w` cells with `3 <= p <= g`, excluding the diagonal affine-plane preference
`AP`	affine-plane diagonal route	implemented diagonal prime-power cells `g-g-(g+1)` where affine planes are the preferred exact family
`AG`	affine-space prime-power route	finite-geometry prime-power cells backed by affine-space constructions
`URD`	uniformly resolvable design literature target	paper-derived supplementary targets whose cited achieving family is a URD row
`RGDD`	catalog-backed resolvable group-divisible design	validated explicit schedules whose clean method source is a listed RGDD case, such as `RGDD(99,9,3)` for `11-9-12`
`RGDD4`	block-size-4 maximum-packing / RGDD spectrum route	p=4 maximum-packing cells explained by RBIBD(v,4), 4-RGDD type 3^(v/3), or 4-RGDD type 2^(v/2), excluding named small exceptions
`RBIBD4`	finite-field resolvable BIBD block-size-4 route	implemented `(v,4,1)` RBIBD construction for `v = 3q + 1` with supported prime-power `q`; retained as a lower-level backing route for the RGDD4 report family
`RTD+G`	resolvable transversal design with recursive group-fill lift	implemented lifted cells where an RTD scaffold is filled from a smaller already-constructible instance
`VIS`	visual-only marker	not a solver family; used only for cells outside the scored objective
`?`	unknown / uncatalogued	fallback when a construction result is present but no explicit abbreviation is mapped