Best Known (82−69, 82, s)-Nets in Base 27
(82−69, 82, 96)-Net over F27 — Constructive and digital
Digital (13, 82, 96)-net over F27, using
- t-expansion [i] based on digital (11, 82, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(82−69, 82, 136)-Net over F27 — Digital
Digital (13, 82, 136)-net over F27, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
(82−69, 82, 1320)-Net in Base 27 — Upper bound on s
There is no (13, 82, 1321)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 81, 1321)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 88 464387 608775 464984 570584 928747 816403 076193 481694 190757 207538 014224 455053 413894 369321 955374 066118 527067 019418 790249 > 2781 [i]