Best Known (54−38, 54, s)-Nets in Base 27
(54−38, 54, 96)-Net over F27 — Constructive and digital
Digital (16, 54, 96)-net over F27, using
- t-expansion [i] based on digital (11, 54, 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
(54−38, 54, 116)-Net in Base 27 — Constructive
(16, 54, 116)-net in base 27, using
- 2 times m-reduction [i] based on (16, 56, 116)-net in base 27, using
- base change [i] based on digital (2, 42, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 42, 116)-net over F81, using
(54−38, 54, 144)-Net over F27 — Digital
Digital (16, 54, 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
(54−38, 54, 3557)-Net in Base 27 — Upper bound on s
There is no (16, 54, 3558)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 197167 009768 216619 348115 226877 300247 282107 706854 079855 058034 988500 868943 099345 > 2754 [i]