Best Known (66−25, 66, s)-Nets in Base 27
(66−25, 66, 248)-Net over F27 — Constructive and digital
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
(66−25, 66, 546)-Net in Base 27 — Constructive
(41, 66, 546)-net in base 27, using
- net defined by OOA [i] based on OOA(2766, 546, S27, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(2766, 6553, S27, 25), using
- discarding factors based on OA(2766, 6563, S27, 25), using
- discarding parts of the base [i] based on linear OA(8149, 6563, F81, 25) (dual of [6563, 6514, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- linear OA(8149, 6561, F81, 25) (dual of [6561, 6512, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 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(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(23) [i] based on
- discarding parts of the base [i] based on linear OA(8149, 6563, F81, 25) (dual of [6563, 6514, 26]-code), using
- discarding factors based on OA(2766, 6563, S27, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(2766, 6553, S27, 25), using
(66−25, 66, 3268)-Net over F27 — Digital
Digital (41, 66, 3268)-net over F27, using
(66−25, 66, large)-Net in Base 27 — Upper bound on s
There is no (41, 66, large)-net in base 27, because
- 23 times m-reduction [i] would yield (41, 43, large)-net in base 27, but