Best Known (23, 37, s)-Nets in Base 27
(23, 37, 280)-Net over F27 — Constructive and digital
Digital (23, 37, 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, 1, 28)-net over F27 (see above)
- digital (0, 1, 28)-net over F27 (see above)
- 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, 4, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 7, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 14, 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
(23, 37, 937)-Net in Base 27 — Constructive
(23, 37, 937)-net in base 27, using
- 271 times duplication [i] based on (22, 36, 937)-net in base 27, using
- base change [i] based on digital (13, 27, 937)-net over F81, using
- net defined by OOA [i] based on linear OOA(8127, 937, F81, 14, 14) (dual of [(937, 14), 13091, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(8127, 6559, F81, 14) (dual of [6559, 6532, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using
- an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(8127, 6559, F81, 14) (dual of [6559, 6532, 15]-code), using
- net defined by OOA [i] based on linear OOA(8127, 937, F81, 14, 14) (dual of [(937, 14), 13091, 15]-NRT-code), using
- base change [i] based on digital (13, 27, 937)-net over F81, using
(23, 37, 2591)-Net over F27 — Digital
Digital (23, 37, 2591)-net over F27, using
(23, 37, 4783270)-Net in Base 27 — Upper bound on s
There is no (23, 37, 4783271)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 91297 710178 490258 474828 581765 072096 188224 393901 639339 > 2737 [i]