Best Known (26, 34, s)-Nets in Base 8
(26, 34, 2058)-Net over F8 — Constructive and digital
Digital (26, 34, 2058)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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 (22, 30, 2049)-net over F8, using
- net defined by OOA [i] based on linear OOA(830, 2049, F8, 8, 8) (dual of [(2049, 8), 16362, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(830, 8196, F8, 8) (dual of [8196, 8166, 9]-code), using
- trace code [i] based on linear OA(6415, 4098, F64, 8) (dual of [4098, 4083, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(6413, 4096, F64, 7) (dual of [4096, 4083, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- trace code [i] based on linear OA(6415, 4098, F64, 8) (dual of [4098, 4083, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(830, 8196, F8, 8) (dual of [8196, 8166, 9]-code), using
- net defined by OOA [i] based on linear OOA(830, 2049, F8, 8, 8) (dual of [(2049, 8), 16362, 9]-NRT-code), using
- digital (0, 4, 9)-net over F8, using
(26, 34, 11759)-Net over F8 — Digital
Digital (26, 34, 11759)-net over F8, using
(26, 34, large)-Net in Base 8 — Upper bound on s
There is no (26, 34, large)-net in base 8, because
- 6 times m-reduction [i] would yield (26, 28, large)-net in base 8, but