Best Known (119, 148, s)-Nets in Base 8
(119, 148, 2375)-Net over F8 — Constructive and digital
Digital (119, 148, 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 (97, 126, 2340)-net over F8, using
- net defined by OOA [i] based on linear OOA(8126, 2340, F8, 29, 29) (dual of [(2340, 29), 67734, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8126, 32761, F8, 29) (dual of [32761, 32635, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(8126, 32768, F8, 29) (dual of [32768, 32642, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(8126, 32761, F8, 29) (dual of [32761, 32635, 30]-code), using
- net defined by OOA [i] based on linear OOA(8126, 2340, F8, 29, 29) (dual of [(2340, 29), 67734, 30]-NRT-code), using
- digital (8, 22, 35)-net over F8, using
(119, 148, 4682)-Net in Base 8 — Constructive
(119, 148, 4682)-net in base 8, using
- base change [i] based on digital (82, 111, 4682)-net over F16, using
- net defined by OOA [i] based on linear OOA(16111, 4682, F16, 29, 29) (dual of [(4682, 29), 135667, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(16111, 65549, F16, 29) (dual of [65549, 65438, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(16111, 65550, F16, 29) (dual of [65550, 65439, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(25) [i] based on
- linear OA(16109, 65536, F16, 29) (dual of [65536, 65427, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(1697, 65536, F16, 26) (dual of [65536, 65439, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(28) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(16111, 65550, F16, 29) (dual of [65550, 65439, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(16111, 65549, F16, 29) (dual of [65549, 65438, 30]-code), using
- net defined by OOA [i] based on linear OOA(16111, 4682, F16, 29, 29) (dual of [(4682, 29), 135667, 30]-NRT-code), using
(119, 148, 95818)-Net over F8 — Digital
Digital (119, 148, 95818)-net over F8, using
(119, 148, large)-Net in Base 8 — Upper bound on s
There is no (119, 148, large)-net in base 8, because
- 27 times m-reduction [i] would yield (119, 121, large)-net in base 8, but