Best Known (87−56, 87, s)-Nets in Base 9
(87−56, 87, 78)-Net over F9 — Constructive and digital
Digital (31, 87, 78)-net over F9, using
- t-expansion [i] based on digital (22, 87, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
(87−56, 87, 120)-Net over F9 — Digital
Digital (31, 87, 120)-net over F9, using
- net from sequence [i] based on digital (31, 119)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 31 and N(F) ≥ 120, using
(87−56, 87, 1285)-Net in Base 9 — Upper bound on s
There is no (31, 87, 1286)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 104763 776359 745482 364753 883074 534032 552845 868661 346574 103632 618293 031239 381252 916673 > 987 [i]