Best Known (56, 76, s)-Nets in Base 27
(56, 76, 2054)-Net over F27 — Constructive and digital
Digital (56, 76, 2054)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (8, 18, 86)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- digital (2, 12, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- digital (1, 6, 38)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (38, 58, 1968)-net over F27, using
- net defined by OOA [i] based on linear OOA(2758, 1968, F27, 20, 20) (dual of [(1968, 20), 39302, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2758, 19680, F27, 20) (dual of [19680, 19622, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2758, 19680, F27, 20) (dual of [19680, 19622, 21]-code), using
- net defined by OOA [i] based on linear OOA(2758, 1968, F27, 20, 20) (dual of [(1968, 20), 39302, 21]-NRT-code), using
- digital (8, 18, 86)-net over F27, using
(56, 76, 2085)-Net in Base 27 — Constructive
(56, 76, 2085)-net in base 27, using
- 271 times duplication [i] based on (55, 75, 2085)-net in base 27, using
- (u, u+v)-construction [i] based on
- (6, 16, 116)-net in base 27, using
- base change [i] based on digital (2, 12, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 12, 116)-net over F81, using
- digital (39, 59, 1969)-net over F27, using
- net defined by OOA [i] based on linear OOA(2759, 1969, F27, 20, 20) (dual of [(1969, 20), 39321, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2759, 19690, F27, 20) (dual of [19690, 19631, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(2758, 19683, F27, 20) (dual of [19683, 19625, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2752, 19683, F27, 18) (dual of [19683, 19631, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(271, 7, F27, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- OA 10-folding and stacking [i] based on linear OA(2759, 19690, F27, 20) (dual of [19690, 19631, 21]-code), using
- net defined by OOA [i] based on linear OOA(2759, 1969, F27, 20, 20) (dual of [(1969, 20), 39321, 21]-NRT-code), using
- (6, 16, 116)-net in base 27, using
- (u, u+v)-construction [i] based on
(56, 76, 162077)-Net over F27 — Digital
Digital (56, 76, 162077)-net over F27, using
(56, 76, large)-Net in Base 27 — Upper bound on s
There is no (56, 76, large)-net in base 27, because
- 18 times m-reduction [i] would yield (56, 58, large)-net in base 27, but