Best Known (6, 6+57, s)-Nets in Base 81
(6, 6+57, 160)-Net over F81 — Constructive and digital
Digital (6, 63, 160)-net over F81, using
- t-expansion [i] based on digital (5, 63, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
(6, 6+57, 190)-Net over F81 — Digital
Digital (6, 63, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
(6, 6+57, 2362)-Net in Base 81 — Upper bound on s
There is no (6, 63, 2363)-net in base 81, because
- 1 times m-reduction [i] would yield (6, 62, 2363)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 21396 760402 742324 548332 316387 385369 943369 297389 406507 638280 426593 424399 692127 220871 574176 646825 094998 901705 089805 920321 > 8162 [i]