Best Known (38, 38+23, s)-Nets in Base 27
(38, 38+23, 262)-Net over F27 — Constructive and digital
Digital (38, 61, 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, 11, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (1, 24, 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
(38, 38+23, 596)-Net in Base 27 — Constructive
(38, 61, 596)-net in base 27, using
- 271 times duplication [i] based on (37, 60, 596)-net in base 27, using
- base change [i] based on digital (22, 45, 596)-net over F81, using
- net defined by OOA [i] based on linear OOA(8145, 596, F81, 23, 23) (dual of [(596, 23), 13663, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8145, 6557, F81, 23) (dual of [6557, 6512, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, 6561, F81, 23) (dual of [6561, 6516, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(8145, 6561, F81, 23) (dual of [6561, 6516, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8145, 6557, F81, 23) (dual of [6557, 6512, 24]-code), using
- net defined by OOA [i] based on linear OOA(8145, 596, F81, 23, 23) (dual of [(596, 23), 13663, 24]-NRT-code), using
- base change [i] based on digital (22, 45, 596)-net over F81, using
(38, 38+23, 3252)-Net over F27 — Digital
Digital (38, 61, 3252)-net over F27, using
(38, 38+23, large)-Net in Base 27 — Upper bound on s
There is no (38, 61, large)-net in base 27, because
- 21 times m-reduction [i] would yield (38, 40, large)-net in base 27, but