Best Known (20, 53, s)-Nets in Base 81
(20, 53, 370)-Net over F81 — Constructive and digital
Digital (20, 53, 370)-net over F81, using
- t-expansion [i] based on digital (16, 53, 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
(20, 53, 135519)-Net in Base 81 — Upper bound on s
There is no (20, 53, 135520)-net in base 81, because
- 1 times m-reduction [i] would yield (20, 52, 135520)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 1742 887211 387212 245846 691461 838781 634785 055344 454012 415977 588384 337248 489395 839636 398703 414261 145601 > 8152 [i]