Best Known (32, 32+106, s)-Nets in Base 9
(32, 32+106, 81)-Net over F9 — Constructive and digital
Digital (32, 138, 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
(32, 32+106, 120)-Net over F9 — Digital
Digital (32, 138, 120)-net over F9, using
- t-expansion [i] based on digital (31, 138, 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
- net from sequence [i] based on digital (31, 119)-sequence over F9, using
(32, 32+106, 753)-Net in Base 9 — Upper bound on s
There is no (32, 138, 754)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 497914 062402 736838 674057 291357 595632 808164 569452 993751 420820 113234 514136 611754 397400 341793 534467 405749 620844 545602 181514 173612 586577 > 9138 [i]