Best Known (55−43, 55, s)-Nets in Base 81
(55−43, 55, 172)-Net over F81 — Constructive and digital
Digital (12, 55, 172)-net over F81, using
- t-expansion [i] based on digital (7, 55, 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
(55−43, 55, 298)-Net over F81 — Digital
Digital (12, 55, 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
(55−43, 55, 8758)-Net in Base 81 — Upper bound on s
There is no (12, 55, 8759)-net in base 81, because
- 1 times m-reduction [i] would yield (12, 54, 8759)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 11 449006 611695 475888 366673 633223 550008 703353 569173 518452 499479 993462 222093 198853 965738 979287 627791 995121 > 8154 [i]