Best Known (63, 63+26, s)-Nets in Base 27
(63, 63+26, 1542)-Net over F27 — Constructive and digital
Digital (63, 89, 1542)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- digital (50, 76, 1514)-net over F27, using
- net defined by OOA [i] based on linear OOA(2776, 1514, F27, 26, 26) (dual of [(1514, 26), 39288, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2776, 19682, F27, 26) (dual of [19682, 19606, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2776, 19683, F27, 26) (dual of [19683, 19607, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(2776, 19683, F27, 26) (dual of [19683, 19607, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2776, 19682, F27, 26) (dual of [19682, 19606, 27]-code), using
- net defined by OOA [i] based on linear OOA(2776, 1514, F27, 26, 26) (dual of [(1514, 26), 39288, 27]-NRT-code), using
- digital (0, 13, 28)-net over F27, using
(63, 63+26, 48800)-Net over F27 — Digital
Digital (63, 89, 48800)-net over F27, using
(63, 63+26, large)-Net in Base 27 — Upper bound on s
There is no (63, 89, large)-net in base 27, because
- 24 times m-reduction [i] would yield (63, 65, large)-net in base 27, but