Best Known (58−21, 58, s)-Nets in Base 27
(58−21, 58, 262)-Net over F27 — Constructive and digital
Digital (37, 58, 262)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 28)-net over F27, using
- 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, 5, 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, 10, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (1, 22, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
(58−21, 58, 656)-Net in Base 27 — Constructive
(37, 58, 656)-net in base 27, using
- 272 times duplication [i] based on (35, 56, 656)-net in base 27, using
- base change [i] based on digital (21, 42, 656)-net over F81, using
- 811 times duplication [i] based on digital (20, 41, 656)-net over F81, using
- net defined by OOA [i] based on linear OOA(8141, 656, F81, 21, 21) (dual of [(656, 21), 13735, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8141, 6561, F81, 21) (dual of [6561, 6520, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- OOA 10-folding and stacking with additional row [i] based on linear OA(8141, 6561, F81, 21) (dual of [6561, 6520, 22]-code), using
- net defined by OOA [i] based on linear OOA(8141, 656, F81, 21, 21) (dual of [(656, 21), 13735, 22]-NRT-code), using
- 811 times duplication [i] based on digital (20, 41, 656)-net over F81, using
- base change [i] based on digital (21, 42, 656)-net over F81, using
(58−21, 58, 4532)-Net over F27 — Digital
Digital (37, 58, 4532)-net over F27, using
(58−21, 58, large)-Net in Base 27 — Upper bound on s
There is no (37, 58, large)-net in base 27, because
- 19 times m-reduction [i] would yield (37, 39, large)-net in base 27, but