Best Known (87, 87+19, s)-Nets in Base 7
(87, 87+19, 13080)-Net over F7 — Constructive and digital
Digital (87, 106, 13080)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (78, 97, 13072)-net over F7, using
- net defined by OOA [i] based on linear OOA(797, 13072, F7, 19, 19) (dual of [(13072, 19), 248271, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(797, 117649, F7, 19) (dual of [117649, 117552, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(797, 117649, F7, 19) (dual of [117649, 117552, 20]-code), using
- net defined by OOA [i] based on linear OOA(797, 13072, F7, 19, 19) (dual of [(13072, 19), 248271, 20]-NRT-code), using
- digital (0, 9, 8)-net over F7, using
(87, 87+19, 119316)-Net over F7 — Digital
Digital (87, 106, 119316)-net over F7, using
(87, 87+19, large)-Net in Base 7 — Upper bound on s
There is no (87, 106, large)-net in base 7, because
- 17 times m-reduction [i] would yield (87, 89, large)-net in base 7, but