Best Known (43, 43+58, s)-Nets in Base 9
(43, 43+58, 81)-Net over F9 — Constructive and digital
Digital (43, 101, 81)-net over F9, using
- t-expansion [i] based on digital (32, 101, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(43, 43+58, 88)-Net in Base 9 — Constructive
(43, 101, 88)-net in base 9, using
- 1 times m-reduction [i] based on (43, 102, 88)-net in base 9, using
- base change [i] based on digital (9, 68, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- base change [i] based on digital (9, 68, 88)-net over F27, using
(43, 43+58, 147)-Net over F9 — Digital
Digital (43, 101, 147)-net over F9, using
- net from sequence [i] based on digital (43, 146)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 43 and N(F) ≥ 147, using
(43, 43+58, 3054)-Net in Base 9 — Upper bound on s
There is no (43, 101, 3055)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 2 402843 345114 810923 011228 928331 266381 973398 192079 843285 364267 461124 474708 645270 750747 685831 253145 > 9101 [i]