Best Known (21, 21+12, s)-Nets in Base 27
(21, 21+12, 280)-Net over F27 — Constructive and digital
Digital (21, 33, 280)-net over F27, using
- 1 times m-reduction [i] based on digital (21, 34, 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, 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, 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, 6, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 13, 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
- generalized (u, u+v)-construction [i] based on
(21, 21+12, 1094)-Net in Base 27 — Constructive
(21, 33, 1094)-net in base 27, using
- 271 times duplication [i] based on (20, 32, 1094)-net in base 27, using
- base change [i] based on digital (12, 24, 1094)-net over F81, using
- net defined by OOA [i] based on linear OOA(8124, 1094, F81, 12, 12) (dual of [(1094, 12), 13104, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(8124, 6564, F81, 12) (dual of [6564, 6540, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(8124, 6566, F81, 12) (dual of [6566, 6542, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(8123, 6561, F81, 12) (dual of [6561, 6538, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(8119, 6561, F81, 10) (dual of [6561, 6542, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(8124, 6566, F81, 12) (dual of [6566, 6542, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(8124, 6564, F81, 12) (dual of [6564, 6540, 13]-code), using
- net defined by OOA [i] based on linear OOA(8124, 1094, F81, 12, 12) (dual of [(1094, 12), 13104, 13]-NRT-code), using
- base change [i] based on digital (12, 24, 1094)-net over F81, using
(21, 21+12, 3722)-Net over F27 — Digital
Digital (21, 33, 3722)-net over F27, using
(21, 21+12, large)-Net in Base 27 — Upper bound on s
There is no (21, 33, large)-net in base 27, because
- 10 times m-reduction [i] would yield (21, 23, large)-net in base 27, but