Best Known (21, 21+39, s)-Nets in Base 81
(21, 21+39, 370)-Net over F81 — Constructive and digital
Digital (21, 60, 370)-net over F81, using
- t-expansion [i] based on digital (16, 60, 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
(21, 21+39, 83642)-Net in Base 81 — Upper bound on s
There is no (21, 60, 83643)-net in base 81, because
- 1 times m-reduction [i] would yield (21, 59, 83643)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 39873 906459 583596 325612 759843 071821 694789 584311 612810 788044 439222 740654 493272 515652 612449 282879 679897 260038 599761 > 8159 [i]