Best Known (37, 37+44, s)-Nets in Base 81
(37, 37+44, 730)-Net over F81 — Constructive and digital
Digital (37, 81, 730)-net over F81, using
- t-expansion [i] based on digital (36, 81, 730)-net over F81, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- the Hermitian function field over F81 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 36 and N(F) ≥ 730, using
- net from sequence [i] based on digital (36, 729)-sequence over F81, using
(37, 37+44, 852)-Net over F81 — Digital
Digital (37, 81, 852)-net over F81, using
(37, 37+44, 1203521)-Net in Base 81 — Upper bound on s
There is no (37, 81, 1203522)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 38662 274228 767228 471523 023795 831831 330661 421742 182469 619707 846256 968502 848939 957108 044642 904626 388250 694306 559045 722577 403602 335377 191771 066359 360335 753921 > 8181 [i]