Best Known (59−16, 59, s)-Nets in Base 27
(59−16, 59, 2528)-Net over F27 — Constructive and digital
Digital (43, 59, 2528)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (5, 13, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (30, 46, 2460)-net over F27, using
- net defined by OOA [i] based on linear OOA(2746, 2460, F27, 16, 16) (dual of [(2460, 16), 39314, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2746, 19680, F27, 16) (dual of [19680, 19634, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2746, 19683, F27, 16) (dual of [19683, 19637, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2746, 19683, F27, 16) (dual of [19683, 19637, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2746, 19680, F27, 16) (dual of [19680, 19634, 17]-code), using
- net defined by OOA [i] based on linear OOA(2746, 2460, F27, 16, 16) (dual of [(2460, 16), 39314, 17]-NRT-code), using
- digital (5, 13, 68)-net over F27, using
(59−16, 59, 2561)-Net in Base 27 — Constructive
(43, 59, 2561)-net in base 27, using
- (u, u+v)-construction [i] based on
- (4, 12, 100)-net in base 27, using
- base change [i] based on digital (1, 9, 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, 9, 100)-net over F81, using
- digital (31, 47, 2461)-net over F27, using
- net defined by OOA [i] based on linear OOA(2747, 2461, F27, 16, 16) (dual of [(2461, 16), 39329, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2747, 19688, F27, 16) (dual of [19688, 19641, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2747, 19690, F27, 16) (dual of [19690, 19643, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(2746, 19683, F27, 16) (dual of [19683, 19637, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2740, 19683, F27, 14) (dual of [19683, 19643, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(2747, 19690, F27, 16) (dual of [19690, 19643, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2747, 19688, F27, 16) (dual of [19688, 19641, 17]-code), using
- net defined by OOA [i] based on linear OOA(2747, 2461, F27, 16, 16) (dual of [(2461, 16), 39329, 17]-NRT-code), using
- (4, 12, 100)-net in base 27, using
(59−16, 59, 105403)-Net over F27 — Digital
Digital (43, 59, 105403)-net over F27, using
(59−16, 59, large)-Net in Base 27 — Upper bound on s
There is no (43, 59, large)-net in base 27, because
- 14 times m-reduction [i] would yield (43, 45, large)-net in base 27, but