Best Known (56, 56+23, s)-Nets in Base 27
(56, 56+23, 1827)-Net over F27 — Constructive and digital
Digital (56, 79, 1827)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 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 (44, 67, 1789)-net over F27, using
- net defined by OOA [i] based on linear OOA(2767, 1789, F27, 23, 23) (dual of [(1789, 23), 41080, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2767, 19680, F27, 23) (dual of [19680, 19613, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2767, 19683, F27, 23) (dual of [19683, 19616, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(2767, 19683, F27, 23) (dual of [19683, 19616, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2767, 19680, F27, 23) (dual of [19680, 19613, 24]-code), using
- net defined by OOA [i] based on linear OOA(2767, 1789, F27, 23, 23) (dual of [(1789, 23), 41080, 24]-NRT-code), using
- digital (1, 12, 38)-net over F27, using
(56, 56+23, 48070)-Net over F27 — Digital
Digital (56, 79, 48070)-net over F27, using
(56, 56+23, large)-Net in Base 27 — Upper bound on s
There is no (56, 79, large)-net in base 27, because
- 21 times m-reduction [i] would yield (56, 58, large)-net in base 27, but