Best Known (15, 15+29, s)-Nets in Base 81
(15, 15+29, 224)-Net over F81 — Constructive and digital
Digital (15, 44, 224)-net over F81, using
- t-expansion [i] based on digital (13, 44, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
(15, 15+29, 298)-Net over F81 — Digital
Digital (15, 44, 298)-net over F81, using
- t-expansion [i] based on digital (12, 44, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
(15, 15+29, 54965)-Net in Base 81 — Upper bound on s
There is no (15, 44, 54966)-net in base 81, because
- 1 times m-reduction [i] would yield (15, 43, 54966)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 11612 016223 463339 801852 069562 355630 231731 611720 933434 043089 603968 689498 958217 536321 > 8143 [i]