Best Known (59, 81, s)-Nets in Base 27
(59, 81, 1865)-Net over F27 — Constructive and digital
Digital (59, 81, 1865)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 17, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (42, 64, 1789)-net over F27, using
- net defined by OOA [i] based on linear OOA(2764, 1789, F27, 22, 22) (dual of [(1789, 22), 39294, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2764, 19679, F27, 22) (dual of [19679, 19615, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2764, 19683, F27, 22) (dual of [19683, 19619, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(2764, 19683, F27, 22) (dual of [19683, 19619, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2764, 19679, F27, 22) (dual of [19679, 19615, 23]-code), using
- net defined by OOA [i] based on linear OOA(2764, 1789, F27, 22, 22) (dual of [(1789, 22), 39294, 23]-NRT-code), using
- digital (6, 17, 76)-net over F27, using
(59, 81, 1890)-Net in Base 27 — Constructive
(59, 81, 1890)-net in base 27, using
- (u, u+v)-construction [i] based on
- (5, 16, 100)-net in base 27, using
- base change [i] based on digital (1, 12, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- base change [i] based on digital (1, 12, 100)-net over F81, using
- digital (43, 65, 1790)-net over F27, using
- net defined by OOA [i] based on linear OOA(2765, 1790, F27, 22, 22) (dual of [(1790, 22), 39315, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2765, 19690, F27, 22) (dual of [19690, 19625, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(2764, 19683, F27, 22) (dual of [19683, 19619, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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(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(21) ⊂ Ce(19) [i] based on
- OA 11-folding and stacking [i] based on linear OA(2765, 19690, F27, 22) (dual of [19690, 19625, 23]-code), using
- net defined by OOA [i] based on linear OOA(2765, 1790, F27, 22, 22) (dual of [(1790, 22), 39315, 23]-NRT-code), using
- (5, 16, 100)-net in base 27, using
(59, 81, 110799)-Net over F27 — Digital
Digital (59, 81, 110799)-net over F27, using
(59, 81, large)-Net in Base 27 — Upper bound on s
There is no (59, 81, large)-net in base 27, because
- 20 times m-reduction [i] would yield (59, 61, large)-net in base 27, but