Best Known (90−19, 90, s)-Nets in Base 8
(90−19, 90, 3650)-Net over F8 — Constructive and digital
Digital (71, 90, 3650)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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]
- a shift-net [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (62, 81, 3641)-net over F8, using
- net defined by OOA [i] based on linear OOA(881, 3641, F8, 19, 19) (dual of [(3641, 19), 69098, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(881, 32770, F8, 19) (dual of [32770, 32689, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(881, 32773, F8, 19) (dual of [32773, 32692, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(881, 32768, F8, 19) (dual of [32768, 32687, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(876, 32768, F8, 18) (dual of [32768, 32692, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(18) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(881, 32773, F8, 19) (dual of [32773, 32692, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(881, 32770, F8, 19) (dual of [32770, 32689, 20]-code), using
- net defined by OOA [i] based on linear OOA(881, 3641, F8, 19, 19) (dual of [(3641, 19), 69098, 20]-NRT-code), using
- digital (0, 9, 9)-net over F8, using
(90−19, 90, 35366)-Net over F8 — Digital
Digital (71, 90, 35366)-net over F8, using
(90−19, 90, large)-Net in Base 8 — Upper bound on s
There is no (71, 90, large)-net in base 8, because
- 17 times m-reduction [i] would yield (71, 73, large)-net in base 8, but