Best Known (57−21, 57, s)-Nets in Base 27
(57−21, 57, 256)-Net over F27 — Constructive and digital
Digital (36, 57, 256)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (2, 7, 64)-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 (4, 11, 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, 14, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 25, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (2, 7, 64)-net over F27, using
(57−21, 57, 656)-Net in Base 27 — Constructive
(36, 57, 656)-net in base 27, using
- 271 times duplication [i] based on (35, 56, 656)-net in base 27, using
- base change [i] based on digital (21, 42, 656)-net over F81, using
- 811 times duplication [i] based on digital (20, 41, 656)-net over F81, using
- net defined by OOA [i] based on linear OOA(8141, 656, F81, 21, 21) (dual of [(656, 21), 13735, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on 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]
- OOA 10-folding and stacking with additional row [i] based on linear OA(8141, 6561, F81, 21) (dual of [6561, 6520, 22]-code), using
- net defined by OOA [i] based on linear OOA(8141, 656, F81, 21, 21) (dual of [(656, 21), 13735, 22]-NRT-code), using
- 811 times duplication [i] based on digital (20, 41, 656)-net over F81, using
- base change [i] based on digital (21, 42, 656)-net over F81, using
(57−21, 57, 3845)-Net over F27 — Digital
Digital (36, 57, 3845)-net over F27, using
(57−21, 57, large)-Net in Base 27 — Upper bound on s
There is no (36, 57, large)-net in base 27, because
- 19 times m-reduction [i] would yield (36, 38, large)-net in base 27, but