Best Known (68, 80, s)-Nets in Base 7
(68, 80, 137274)-Net over F7 — Constructive and digital
Digital (68, 80, 137274)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 16)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 8)-net over F7, using
- net from sequence [i] based on digital (0, 7)-sequence over F7, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using
- the rational function field F7(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 7)-sequence over F7, using
- digital (0, 6, 8)-net over F7, using
- net from sequence [i] based on digital (0, 7)-sequence over F7 (see above)
- digital (0, 3, 8)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (59, 71, 137258)-net over F7, using
- net defined by OOA [i] based on linear OOA(771, 137258, F7, 12, 12) (dual of [(137258, 12), 1647025, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(771, 823548, F7, 12) (dual of [823548, 823477, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(771, 823550, F7, 12) (dual of [823550, 823479, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(771, 823543, F7, 12) (dual of [823543, 823472, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(764, 823543, F7, 11) (dual of [823543, 823479, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(70, 7, F7, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(771, 823550, F7, 12) (dual of [823550, 823479, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(771, 823548, F7, 12) (dual of [823548, 823477, 13]-code), using
- net defined by OOA [i] based on linear OOA(771, 137258, F7, 12, 12) (dual of [(137258, 12), 1647025, 13]-NRT-code), using
- digital (3, 9, 16)-net over F7, using
(68, 80, 1145599)-Net over F7 — Digital
Digital (68, 80, 1145599)-net over F7, using
(68, 80, large)-Net in Base 7 — Upper bound on s
There is no (68, 80, large)-net in base 7, because
- 10 times m-reduction [i] would yield (68, 70, large)-net in base 7, but