Best Known (51−19, 51, s)-Nets in Base 27
(51−19, 51, 280)-Net over F27 — Constructive and digital
Digital (32, 51, 280)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 28)-net over F27, using
- s-reduction based on digital (0, 1, s)-net over F27 with arbitrarily large s, using
- digital (0, 2, 28)-net over F27, using
- digital (0, 2, 28)-net over F27 (see above)
- digital (0, 2, 28)-net over F27 (see above)
- digital (0, 3, 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 (0, 3, 28)-net over F27 (see above)
- digital (0, 4, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 6, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 9, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 19, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 1, 28)-net over F27, using
(51−19, 51, 729)-Net in Base 27 — Constructive
(32, 51, 729)-net in base 27, using
- 271 times duplication [i] based on (31, 50, 729)-net in base 27, using
- net defined by OOA [i] based on OOA(2750, 729, S27, 19, 19), using
- OOA 9-folding and stacking with additional row [i] based on OA(2750, 6562, S27, 19), using
- discarding factors based on OA(2750, 6563, S27, 19), using
- discarding parts of the base [i] based on linear OA(8137, 6563, F81, 19) (dual of [6563, 6526, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(8137, 6561, F81, 19) (dual of [6561, 6524, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- discarding parts of the base [i] based on linear OA(8137, 6563, F81, 19) (dual of [6563, 6526, 20]-code), using
- discarding factors based on OA(2750, 6563, S27, 19), using
- OOA 9-folding and stacking with additional row [i] based on OA(2750, 6562, S27, 19), using
- net defined by OOA [i] based on OOA(2750, 729, S27, 19, 19), using
(51−19, 51, 3310)-Net over F27 — Digital
Digital (32, 51, 3310)-net over F27, using
(51−19, 51, large)-Net in Base 27 — Upper bound on s
There is no (32, 51, large)-net in base 27, because
- 17 times m-reduction [i] would yield (32, 34, large)-net in base 27, but