Best Known (56−20, 56, s)-Nets in Base 81
(56−20, 56, 856)-Net over F81 — Constructive and digital
Digital (36, 56, 856)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (7, 17, 200)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 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 (1, 11, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81 (see above)
- digital (1, 6, 100)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (19, 39, 656)-net over F81, using
- net defined by OOA [i] based on linear OOA(8139, 656, F81, 20, 20) (dual of [(656, 20), 13081, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(8139, 6560, F81, 20) (dual of [6560, 6521, 21]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(8139, 6560, F81, 20) (dual of [6560, 6521, 21]-code), using
- net defined by OOA [i] based on linear OOA(8139, 656, F81, 20, 20) (dual of [(656, 20), 13081, 21]-NRT-code), using
- digital (7, 17, 200)-net over F81, using
(56−20, 56, 41805)-Net over F81 — Digital
Digital (36, 56, 41805)-net over F81, using
(56−20, 56, large)-Net in Base 81 — Upper bound on s
There is no (36, 56, large)-net in base 81, because
- 18 times m-reduction [i] would yield (36, 38, large)-net in base 81, but