Best Known (65, 65+20, s)-Nets in Base 9
(65, 65+20, 1314)-Net over F9 — Constructive and digital
Digital (65, 85, 1314)-net over F9, using
- 91 times duplication [i] based on digital (64, 84, 1314)-net over F9, using
- net defined by OOA [i] based on linear OOA(984, 1314, F9, 20, 20) (dual of [(1314, 20), 26196, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(984, 13140, F9, 20) (dual of [13140, 13056, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(984, 13144, F9, 20) (dual of [13144, 13060, 21]-code), using
- trace code [i] based on linear OA(8142, 6572, F81, 20) (dual of [6572, 6530, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(15) [i] based on
- linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(19) ⊂ Ce(15) [i] based on
- trace code [i] based on linear OA(8142, 6572, F81, 20) (dual of [6572, 6530, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(984, 13144, F9, 20) (dual of [13144, 13060, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(984, 13140, F9, 20) (dual of [13140, 13056, 21]-code), using
- net defined by OOA [i] based on linear OOA(984, 1314, F9, 20, 20) (dual of [(1314, 20), 26196, 21]-NRT-code), using
(65, 65+20, 18422)-Net over F9 — Digital
Digital (65, 85, 18422)-net over F9, using
(65, 65+20, large)-Net in Base 9 — Upper bound on s
There is no (65, 85, large)-net in base 9, because
- 18 times m-reduction [i] would yield (65, 67, large)-net in base 9, but