Best Known (132−26, 132, s)-Nets in Base 8
(132−26, 132, 2556)-Net over F8 — Constructive and digital
Digital (106, 132, 2556)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 21, 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 (85, 111, 2521)-net over F8, using
- net defined by OOA [i] based on linear OOA(8111, 2521, F8, 26, 26) (dual of [(2521, 26), 65435, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8111, 32773, F8, 26) (dual of [32773, 32662, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- OA 13-folding and stacking [i] based on linear OA(8111, 32773, F8, 26) (dual of [32773, 32662, 27]-code), using
- net defined by OOA [i] based on linear OOA(8111, 2521, F8, 26, 26) (dual of [(2521, 26), 65435, 27]-NRT-code), using
- digital (8, 21, 35)-net over F8, using
(132−26, 132, 5042)-Net in Base 8 — Constructive
(106, 132, 5042)-net in base 8, using
- base change [i] based on digital (73, 99, 5042)-net over F16, using
- net defined by OOA [i] based on linear OOA(1699, 5042, F16, 26, 26) (dual of [(5042, 26), 130993, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(1699, 65546, F16, 26) (dual of [65546, 65447, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(1699, 65550, F16, 26) (dual of [65550, 65451, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(22) [i] based on
- 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(1685, 65536, F16, 23) (dual of [65536, 65451, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(25) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(1699, 65550, F16, 26) (dual of [65550, 65451, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(1699, 65546, F16, 26) (dual of [65546, 65447, 27]-code), using
- net defined by OOA [i] based on linear OOA(1699, 5042, F16, 26, 26) (dual of [(5042, 26), 130993, 27]-NRT-code), using
(132−26, 132, 85292)-Net over F8 — Digital
Digital (106, 132, 85292)-net over F8, using
(132−26, 132, large)-Net in Base 8 — Upper bound on s
There is no (106, 132, large)-net in base 8, because
- 24 times m-reduction [i] would yield (106, 108, large)-net in base 8, but