Best Known (30−12, 30, s)-Nets in Base 81
(30−12, 30, 1193)-Net over F81 — Constructive and digital
Digital (18, 30, 1193)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- digital (11, 23, 1093)-net over F81, using
- net defined by OOA [i] based on linear OOA(8123, 1093, F81, 12, 12) (dual of [(1093, 12), 13093, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(8123, 6558, F81, 12) (dual of [6558, 6535, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(8123, 6561, F81, 12) (dual of [6561, 6538, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(8123, 6561, F81, 12) (dual of [6561, 6538, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(8123, 6558, F81, 12) (dual of [6558, 6535, 13]-code), using
- net defined by OOA [i] based on linear OOA(8123, 1093, F81, 12, 12) (dual of [(1093, 12), 13093, 13]-NRT-code), using
- digital (1, 7, 100)-net over F81, using
(30−12, 30, 9843)-Net over F81 — Digital
Digital (18, 30, 9843)-net over F81, using
(30−12, 30, large)-Net in Base 81 — Upper bound on s
There is no (18, 30, large)-net in base 81, because
- 10 times m-reduction [i] would yield (18, 20, large)-net in base 81, but