Best Known (36, 36+45, s)-Nets in Base 81
(36, 36+45, 730)-Net over F81 — Constructive and digital
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
(36, 36+45, 985607)-Net in Base 81 — Upper bound on s
There is no (36, 81, 985608)-net in base 81, because
- 1 times m-reduction [i] would yield (36, 80, 985608)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 477 320857 000363 630064 400830 840382 706350 751932 940380 006660 582500 550371 580365 472372 548238 902677 590988 690496 004190 237350 548230 730587 594954 766423 790495 732481 > 8180 [i]