Best Known (126−19, 126, s)-Nets in Base 8
(126−19, 126, 233042)-Net over F8 — Constructive and digital
Digital (107, 126, 233042)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (4, 13, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- digital (94, 113, 233017)-net over F8, using
- net defined by OOA [i] based on linear OOA(8113, 233017, F8, 19, 19) (dual of [(233017, 19), 4427210, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8113, 2097154, F8, 19) (dual of [2097154, 2097041, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8113, 2097159, F8, 19) (dual of [2097159, 2097046, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(8113, 2097152, F8, 19) (dual of [2097152, 2097039, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(8106, 2097152, F8, 18) (dual of [2097152, 2097046, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(80, 7, F8, 0) (dual of [7, 7, 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(18) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(8113, 2097159, F8, 19) (dual of [2097159, 2097046, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8113, 2097154, F8, 19) (dual of [2097154, 2097041, 20]-code), using
- net defined by OOA [i] based on linear OOA(8113, 233017, F8, 19, 19) (dual of [(233017, 19), 4427210, 20]-NRT-code), using
- digital (4, 13, 25)-net over F8, using
(126−19, 126, 2262891)-Net over F8 — Digital
Digital (107, 126, 2262891)-net over F8, using
(126−19, 126, large)-Net in Base 8 — Upper bound on s
There is no (107, 126, large)-net in base 8, because
- 17 times m-reduction [i] would yield (107, 109, large)-net in base 8, but