Best Known (65−56, 65, s)-Nets in Base 81
(65−56, 65, 172)-Net over F81 — Constructive and digital
Digital (9, 65, 172)-net over F81, using
- t-expansion [i] based on digital (7, 65, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(65−56, 65, 244)-Net over F81 — Digital
Digital (9, 65, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
(65−56, 65, 3790)-Net in Base 81 — Upper bound on s
There is no (9, 65, 3791)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 11266 746491 644276 182525 435349 672412 519478 275061 690909 448028 839918 423609 671974 554318 074405 114434 832345 209672 035194 035038 815041 > 8165 [i]