Best Known (41, 65, s)-Nets in Base 27
(41, 65, 248)-Net over F27 — Constructive and digital
Digital (41, 65, 248)-net over F27, using
- 1 times m-reduction [i] based on digital (41, 66, 248)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (3, 9, 56)-net over F27, using
- (u, u+v)-construction [i] based on
- 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, 6, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27 (see above)
- digital (0, 3, 28)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (4, 16, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 29, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (3, 9, 56)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(41, 65, 547)-Net in Base 27 — Constructive
(41, 65, 547)-net in base 27, using
- 271 times duplication [i] based on (40, 64, 547)-net in base 27, using
- base change [i] based on digital (24, 48, 547)-net over F81, using
- net defined by OOA [i] based on linear OOA(8148, 547, F81, 24, 24) (dual of [(547, 24), 13080, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(8148, 6564, F81, 24) (dual of [6564, 6516, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8148, 6566, F81, 24) (dual of [6566, 6518, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(8147, 6561, F81, 24) (dual of [6561, 6514, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8148, 6566, F81, 24) (dual of [6566, 6518, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(8148, 6564, F81, 24) (dual of [6564, 6516, 25]-code), using
- net defined by OOA [i] based on linear OOA(8148, 547, F81, 24, 24) (dual of [(547, 24), 13080, 25]-NRT-code), using
- base change [i] based on digital (24, 48, 547)-net over F81, using
(41, 65, 4035)-Net over F27 — Digital
Digital (41, 65, 4035)-net over F27, using
(41, 65, large)-Net in Base 27 — Upper bound on s
There is no (41, 65, large)-net in base 27, because
- 22 times m-reduction [i] would yield (41, 43, large)-net in base 27, but