Best Known (63−13, 63, s)-Nets in Base 8
(63−13, 63, 5476)-Net over F8 — Constructive and digital
Digital (50, 63, 5476)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 14)-net over F8, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- digital (43, 56, 5462)-net over F8, using
- net defined by OOA [i] based on linear OOA(856, 5462, F8, 13, 13) (dual of [(5462, 13), 70950, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(856, 32773, F8, 13) (dual of [32773, 32717, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(856, 32768, F8, 13) (dual of [32768, 32712, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(851, 32768, F8, 12) (dual of [32768, 32717, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(12) ⊂ Ce(11) [i] based on
- OOA 6-folding and stacking with additional row [i] based on linear OA(856, 32773, F8, 13) (dual of [32773, 32717, 14]-code), using
- net defined by OOA [i] based on linear OOA(856, 5462, F8, 13, 13) (dual of [(5462, 13), 70950, 14]-NRT-code), using
- digital (1, 7, 14)-net over F8, using
(63−13, 63, 41643)-Net over F8 — Digital
Digital (50, 63, 41643)-net over F8, using
(63−13, 63, large)-Net in Base 8 — Upper bound on s
There is no (50, 63, large)-net in base 8, because
- 11 times m-reduction [i] would yield (50, 52, large)-net in base 8, but