Best Known (83, 101, s)-Nets in Base 7
(83, 101, 13085)-Net over F7 — Constructive and digital
Digital (83, 101, 13085)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 13)-net over F7, using
- 3 times m-reduction [i] based on digital (1, 13, 13)-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 (1, 10, 13)-net over F7, using
(83, 101, 125516)-Net over F7 — Digital
Digital (83, 101, 125516)-net over F7, using
(83, 101, large)-Net in Base 7 — Upper bound on s
There is no (83, 101, large)-net in base 7, because
- 16 times m-reduction [i] would yield (83, 85, large)-net in base 7, but