Best Known (126−22, 126, s)-Nets in Base 8
(126−22, 126, 23840)-Net over F8 — Constructive and digital
Digital (104, 126, 23840)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (93, 115, 23831)-net over F8, using
- net defined by OOA [i] based on linear OOA(8115, 23831, F8, 22, 22) (dual of [(23831, 22), 524167, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8115, 262141, F8, 22) (dual of [262141, 262026, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(8115, 262144, F8, 22) (dual of [262144, 262029, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8115, 262141, F8, 22) (dual of [262141, 262026, 23]-code), using
- net defined by OOA [i] based on linear OOA(8115, 23831, F8, 22, 22) (dual of [(23831, 22), 524167, 23]-NRT-code), using
- digital (0, 11, 9)-net over F8, using
(126−22, 126, 325049)-Net over F8 — Digital
Digital (104, 126, 325049)-net over F8, using
(126−22, 126, large)-Net in Base 8 — Upper bound on s
There is no (104, 126, large)-net in base 8, because
- 20 times m-reduction [i] would yield (104, 106, large)-net in base 8, but