Best Known (115, 115+28, s)-Nets in Base 8
(115, 115+28, 2375)-Net over F8 — Constructive and digital
Digital (115, 143, 2375)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 22, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- digital (93, 121, 2340)-net over F8, using
- net defined by OOA [i] based on linear OOA(8121, 2340, F8, 28, 28) (dual of [(2340, 28), 65399, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(8121, 32760, F8, 28) (dual of [32760, 32639, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(8121, 32768, F8, 28) (dual of [32768, 32647, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(8121, 32760, F8, 28) (dual of [32760, 32639, 29]-code), using
- net defined by OOA [i] based on linear OOA(8121, 2340, F8, 28, 28) (dual of [(2340, 28), 65399, 29]-NRT-code), using
- digital (8, 22, 35)-net over F8, using
(115, 115+28, 4682)-Net in Base 8 — Constructive
(115, 143, 4682)-net in base 8, using
- net defined by OOA [i] based on OOA(8143, 4682, S8, 28, 28), using
- OA 14-folding and stacking [i] based on OA(8143, 65548, S8, 28), using
- discarding factors based on OA(8143, 65550, S8, 28), using
- discarding parts of the base [i] based on linear OA(16107, 65550, F16, 28) (dual of [65550, 65443, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(1693, 65536, F16, 25) (dual of [65536, 65443, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- discarding parts of the base [i] based on linear OA(16107, 65550, F16, 28) (dual of [65550, 65443, 29]-code), using
- discarding factors based on OA(8143, 65550, S8, 28), using
- OA 14-folding and stacking [i] based on OA(8143, 65548, S8, 28), using
(115, 115+28, 94711)-Net over F8 — Digital
Digital (115, 143, 94711)-net over F8, using
(115, 115+28, large)-Net in Base 8 — Upper bound on s
There is no (115, 143, large)-net in base 8, because
- 26 times m-reduction [i] would yield (115, 117, large)-net in base 8, but