Best Known (36, 58, s)-Nets in Base 27
(36, 58, 240)-Net over F27 — Constructive and digital
Digital (36, 58, 240)-net over F27, using
- 1 times m-reduction [i] based on digital (36, 59, 240)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (2, 7, 56)-net over F27, using
- s-reduction based on digital (2, 7, 351)-net over F27, using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- s-reduction based on digital (2, 7, 351)-net over F27, using
- digital (3, 10, 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, 7, 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, 15, 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, 27, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (2, 7, 56)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(36, 58, 596)-Net in Base 27 — Constructive
(36, 58, 596)-net in base 27, using
- net defined by OOA [i] based on OOA(2758, 596, S27, 22, 22), using
- OA 11-folding and stacking [i] based on OA(2758, 6556, S27, 22), using
- discarding factors based on OA(2758, 6563, S27, 22), using
- discarding parts of the base [i] based on linear OA(8143, 6563, F81, 22) (dual of [6563, 6520, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- 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(8141, 6561, F81, 21) (dual of [6561, 6520, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(21) ⊂ Ce(20) [i] based on
- discarding parts of the base [i] based on linear OA(8143, 6563, F81, 22) (dual of [6563, 6520, 23]-code), using
- discarding factors based on OA(2758, 6563, S27, 22), using
- OA 11-folding and stacking [i] based on OA(2758, 6556, S27, 22), using
(36, 58, 3008)-Net over F27 — Digital
Digital (36, 58, 3008)-net over F27, using
(36, 58, 6656274)-Net in Base 27 — Upper bound on s
There is no (36, 58, 6656275)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 104495 796527 216471 561181 514957 656868 019457 079723 213940 978859 448824 395731 241443 118451 > 2758 [i]