Best Known (57−30, 57, s)-Nets in Base 81
(57−30, 57, 370)-Net over F81 — Constructive and digital
Digital (27, 57, 370)-net over F81, using
- t-expansion [i] based on digital (16, 57, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(57−30, 57, 837)-Net over F81 — Digital
Digital (27, 57, 837)-net over F81, using
(57−30, 57, 1435216)-Net in Base 81 — Upper bound on s
There is no (27, 57, 1435217)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 6 076400 154515 818696 182385 165079 747719 307940 675688 374415 589725 195058 083627 344913 453759 970966 006931 961860 916401 > 8157 [i]