Best Known (18, 64, s)-Nets in Base 27
(18, 64, 108)-Net over F27 — Constructive and digital
Digital (18, 64, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
(18, 64, 116)-Net in Base 27 — Constructive
(18, 64, 116)-net in base 27, using
- base change [i] based on digital (2, 48, 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
(18, 64, 148)-Net over F27 — Digital
Digital (18, 64, 148)-net over F27, using
- net from sequence [i] based on digital (18, 147)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 148, using
(18, 64, 3474)-Net in Base 27 — Upper bound on s
There is no (18, 64, 3475)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 40 544362 193550 132957 140873 807517 382859 445637 004059 796948 193775 616042 339124 067443 095905 730331 > 2764 [i]