Best Known (56, 56+15, s)-Nets in Base 7
(56, 56+15, 2417)-Net over F7 — Constructive and digital
Digital (56, 71, 2417)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 16)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 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 (0, 7, 8)-net over F7, using
- net from sequence [i] based on digital (0, 7)-sequence over F7 (see above)
- digital (0, 3, 8)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (46, 61, 2401)-net over F7, using
- net defined by OOA [i] based on linear OOA(761, 2401, F7, 15, 15) (dual of [(2401, 15), 35954, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(761, 16808, F7, 15) (dual of [16808, 16747, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(761, 16808, F7, 15) (dual of [16808, 16747, 16]-code), using
- net defined by OOA [i] based on linear OOA(761, 2401, F7, 15, 15) (dual of [(2401, 15), 35954, 16]-NRT-code), using
- digital (3, 10, 16)-net over F7, using
(56, 56+15, 19468)-Net over F7 — Digital
Digital (56, 71, 19468)-net over F7, using
(56, 56+15, large)-Net in Base 7 — Upper bound on s
There is no (56, 71, large)-net in base 7, because
- 13 times m-reduction [i] would yield (56, 58, large)-net in base 7, but