Best Known (72, 72+22, s)-Nets in Base 9
(72, 72+22, 1195)-Net over F9 — Constructive and digital
Digital (72, 94, 1195)-net over F9, using
- 91 times duplication [i] based on digital (71, 93, 1195)-net over F9, using
- net defined by OOA [i] based on linear OOA(993, 1195, F9, 22, 22) (dual of [(1195, 22), 26197, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(993, 13145, F9, 22) (dual of [13145, 13052, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(992, 13144, F9, 22) (dual of [13144, 13052, 23]-code), using
- trace code [i] based on linear OA(8146, 6572, F81, 22) (dual of [6572, 6526, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- trace code [i] based on linear OA(8146, 6572, F81, 22) (dual of [6572, 6526, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(992, 13144, F9, 22) (dual of [13144, 13052, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(993, 13145, F9, 22) (dual of [13145, 13052, 23]-code), using
- net defined by OOA [i] based on linear OOA(993, 1195, F9, 22, 22) (dual of [(1195, 22), 26197, 23]-NRT-code), using
(72, 72+22, 20277)-Net over F9 — Digital
Digital (72, 94, 20277)-net over F9, using
(72, 72+22, large)-Net in Base 9 — Upper bound on s
There is no (72, 94, large)-net in base 9, because
- 20 times m-reduction [i] would yield (72, 74, large)-net in base 9, but