Best Known (85, 85+22, s)-Nets in Base 7
(85, 85+22, 1545)-Net over F7 — Constructive and digital
Digital (85, 107, 1545)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (5, 16, 18)-net over F7, using
- 2 times m-reduction [i] based on digital (5, 18, 18)-net 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 (5, 16, 18)-net over F7, using
(85, 85+22, 29273)-Net over F7 — Digital
Digital (85, 107, 29273)-net over F7, using
(85, 85+22, large)-Net in Base 7 — Upper bound on s
There is no (85, 107, large)-net in base 7, because
- 20 times m-reduction [i] would yield (85, 87, large)-net in base 7, but