Best Known (16, 16+42, s)-Nets in Base 27
(16, 16+42, 96)-Net over F27 — Constructive and digital
Digital (16, 58, 96)-net over F27, using
- t-expansion [i] based on digital (11, 58, 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
(16, 16+42, 100)-Net in Base 27 — Constructive
(16, 58, 100)-net in base 27, using
- 2 times m-reduction [i] based on (16, 60, 100)-net in base 27, using
- base change [i] based on digital (1, 45, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- base change [i] based on digital (1, 45, 100)-net over F81, using
(16, 16+42, 144)-Net over F27 — Digital
Digital (16, 58, 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
(16, 16+42, 2987)-Net in Base 27 — Upper bound on s
There is no (16, 58, 2988)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 105193 827123 279448 712847 206190 138817 018263 763166 302829 949452 873242 389696 745529 573721 > 2758 [i]