Best Known (85, 85+18, s)-Nets in Base 7
(85, 85+18, 13086)-Net over F7 — Constructive and digital
Digital (85, 103, 13086)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (3, 12, 14)-net over F7, using
- 2 times m-reduction [i] based on digital (3, 14, 14)-net over F7, using
- digital (73, 91, 13072)-net over F7, using
- net defined by OOA [i] based on linear OOA(791, 13072, F7, 18, 18) (dual of [(13072, 18), 235205, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(791, 117648, F7, 18) (dual of [117648, 117557, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(791, 117649, F7, 18) (dual of [117649, 117558, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(791, 117649, F7, 18) (dual of [117649, 117558, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(791, 117648, F7, 18) (dual of [117648, 117557, 19]-code), using
- net defined by OOA [i] based on linear OOA(791, 13072, F7, 18, 18) (dual of [(13072, 18), 235205, 19]-NRT-code), using
- digital (3, 12, 14)-net over F7, using
(85, 85+18, 157804)-Net over F7 — Digital
Digital (85, 103, 157804)-net over F7, using
(85, 85+18, large)-Net in Base 7 — Upper bound on s
There is no (85, 103, large)-net in base 7, because
- 16 times m-reduction [i] would yield (85, 87, large)-net in base 7, but