Best Known (80, 80+22, s)-Nets in Base 7
(80, 80+22, 1535)-Net over F7 — Constructive and digital
Digital (80, 102, 1535)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 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 (69, 91, 1527)-net over F7, using
- net defined by OOA [i] based on linear OOA(791, 1527, F7, 22, 22) (dual of [(1527, 22), 33503, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(791, 16797, F7, 22) (dual of [16797, 16706, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(791, 16807, F7, 22) (dual of [16807, 16716, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(791, 16807, F7, 22) (dual of [16807, 16716, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(791, 16797, F7, 22) (dual of [16797, 16706, 23]-code), using
- net defined by OOA [i] based on linear OOA(791, 1527, F7, 22, 22) (dual of [(1527, 22), 33503, 23]-NRT-code), using
- digital (0, 11, 8)-net over F7, using
(80, 80+22, 18422)-Net over F7 — Digital
Digital (80, 102, 18422)-net over F7, using
(80, 80+22, large)-Net in Base 7 — Upper bound on s
There is no (80, 102, large)-net in base 7, because
- 20 times m-reduction [i] would yield (80, 82, large)-net in base 7, but