Best Known (15, 15+30, s)-Nets in Base 81
(15, 15+30, 224)-Net over F81 — Constructive and digital
Digital (15, 45, 224)-net over F81, using
- t-expansion [i] based on digital (13, 45, 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+30, 298)-Net over F81 — Digital
Digital (15, 45, 298)-net over F81, using
- t-expansion [i] based on digital (12, 45, 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+30, 42663)-Net in Base 81 — Upper bound on s
There is no (15, 45, 42664)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 76 185284 078354 262886 995392 077122 457786 279093 304293 490249 148066 854187 572661 483948 156801 > 8145 [i]