Best Known (26, 41, s)-Nets in Base 27
(26, 41, 308)-Net over F27 — Constructive and digital
Digital (26, 41, 308)-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, 3, 28)-net 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, 15, 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
(26, 41, 938)-Net in Base 27 — Constructive
(26, 41, 938)-net in base 27, using
- 271 times duplication [i] based on (25, 40, 938)-net in base 27, using
- base change [i] based on digital (15, 30, 938)-net over F81, using
- net defined by OOA [i] based on linear OOA(8130, 938, F81, 15, 15) (dual of [(938, 15), 14040, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(8130, 6567, F81, 15) (dual of [6567, 6537, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(8129, 6562, F81, 15) (dual of [6562, 6533, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(8125, 6562, F81, 13) (dual of [6562, 6537, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [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 C([0,7]) ⊂ C([0,6]) [i] based on
- OOA 7-folding and stacking with additional row [i] based on linear OA(8130, 6567, F81, 15) (dual of [6567, 6537, 16]-code), using
- net defined by OOA [i] based on linear OOA(8130, 938, F81, 15, 15) (dual of [(938, 15), 14040, 16]-NRT-code), using
- base change [i] based on digital (15, 30, 938)-net over F81, using
(26, 41, 3624)-Net over F27 — Digital
Digital (26, 41, 3624)-net over F27, using
(26, 41, large)-Net in Base 27 — Upper bound on s
There is no (26, 41, large)-net in base 27, because
- 13 times m-reduction [i] would yield (26, 28, large)-net in base 27, but