Best Known (33, 33+116, s)-Nets in Base 9
(33, 33+116, 81)-Net over F9 — Constructive and digital
Digital (33, 149, 81)-net over F9, using
- t-expansion [i] based on digital (32, 149, 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
(33, 33+116, 128)-Net over F9 — Digital
Digital (33, 149, 128)-net over F9, using
- net from sequence [i] based on digital (33, 127)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 33 and N(F) ≥ 128, using
(33, 33+116, 758)-Net in Base 9 — Upper bound on s
There is no (33, 149, 759)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 16099 397080 318153 351828 026236 122531 533508 237837 898915 004496 130063 193338 606863 424892 072967 688846 413618 719522 608475 976247 184894 340114 235775 163569 > 9149 [i]