Best Known (83−67, 83, s)-Nets in Base 27
(83−67, 83, 96)-Net over F27 — Constructive and digital
Digital (16, 83, 96)-net over F27, using
- t-expansion [i] based on digital (11, 83, 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
(83−67, 83, 144)-Net over F27 — Digital
Digital (16, 83, 144)-net over F27, using
- net from sequence [i] based on digital (16, 143)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 16 and N(F) ≥ 144, using
(83−67, 83, 1807)-Net in Base 27 — Upper bound on s
There is no (16, 83, 1808)-net in base 27, because
- 1 times m-reduction [i] would yield (16, 82, 1808)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 2392 976245 770566 616724 815563 105868 335067 657032 859182 359628 032228 044659 622195 951193 195732 136898 670993 273427 078976 644001 > 2782 [i]