Best Known (35−14, 35, s)-Nets in Base 7
(35−14, 35, 108)-Net over F7 — Constructive and digital
Digital (21, 35, 108)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 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 (14, 28, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 14, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- trace code for nets [i] based on digital (0, 14, 50)-net over F49, using
- digital (0, 7, 8)-net over F7, using
(35−14, 35, 193)-Net over F7 — Digital
Digital (21, 35, 193)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(735, 193, F7, 14) (dual of [193, 158, 15]-code), using
- 8 step Varšamov–Edel lengthening with (ri) = (1, 7 times 0) [i] based on linear OA(734, 184, F7, 14) (dual of [184, 150, 15]-code), using
- trace code [i] based on linear OA(4917, 92, F49, 14) (dual of [92, 75, 15]-code), using
- extended algebraic-geometric code AGe(F,77P) [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- trace code [i] based on linear OA(4917, 92, F49, 14) (dual of [92, 75, 15]-code), using
- 8 step Varšamov–Edel lengthening with (ri) = (1, 7 times 0) [i] based on linear OA(734, 184, F7, 14) (dual of [184, 150, 15]-code), using
(35−14, 35, 9463)-Net in Base 7 — Upper bound on s
There is no (21, 35, 9464)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 378869 172116 421000 105424 931521 > 735 [i]