Best Known (6, 6+42, s)-Nets in Base 81
(6, 6+42, 160)-Net over F81 — Constructive and digital
Digital (6, 48, 160)-net over F81, using
- t-expansion [i] based on digital (5, 48, 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+42, 190)-Net over F81 — Digital
Digital (6, 48, 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+42, 2488)-Net in Base 81 — Upper bound on s
There is no (6, 48, 2489)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 40 791014 532170 331054 233171 767783 343522 029364 127894 928694 606917 397681 762899 549053 196401 301521 > 8148 [i]