Best Known (126−25, 126, s)-Nets in Base 8
(126−25, 126, 2765)-Net over F8 — Constructive and digital
Digital (101, 126, 2765)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 20, 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 (81, 106, 2730)-net over F8, using
- net defined by OOA [i] based on linear OOA(8106, 2730, F8, 25, 25) (dual of [(2730, 25), 68144, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8106, 32761, F8, 25) (dual of [32761, 32655, 26]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8106, 32761, F8, 25) (dual of [32761, 32655, 26]-code), using
- net defined by OOA [i] based on linear OOA(8106, 2730, F8, 25, 25) (dual of [(2730, 25), 68144, 26]-NRT-code), using
- digital (8, 20, 35)-net over F8, using
(126−25, 126, 5462)-Net in Base 8 — Constructive
(101, 126, 5462)-net in base 8, using
- net defined by OOA [i] based on OOA(8126, 5462, S8, 25, 25), using
- OOA 12-folding and stacking with additional row [i] based on OA(8126, 65545, S8, 25), using
- discarding parts of the base [i] based on linear OA(1694, 65545, F16, 25) (dual of [65545, 65451, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- 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(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(161, 9, F16, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- discarding parts of the base [i] based on linear OA(1694, 65545, F16, 25) (dual of [65545, 65451, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on OA(8126, 65545, S8, 25), using
(126−25, 126, 77189)-Net over F8 — Digital
Digital (101, 126, 77189)-net over F8, using
(126−25, 126, large)-Net in Base 8 — Upper bound on s
There is no (101, 126, large)-net in base 8, because
- 23 times m-reduction [i] would yield (101, 103, large)-net in base 8, but