Best Known (64−44, 64, s)-Nets in Base 27
(64−44, 64, 108)-Net over F27 — Constructive and digital
Digital (20, 64, 108)-net over F27, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
(64−44, 64, 148)-Net over F27 — Digital
Digital (20, 64, 148)-net over F27, using
- t-expansion [i] based on 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
- net from sequence [i] based on digital (18, 147)-sequence over F27, using
(64−44, 64, 150)-Net in Base 27 — Constructive
(20, 64, 150)-net in base 27, using
- base change [i] based on digital (4, 48, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
(64−44, 64, 154)-Net in Base 27
(20, 64, 154)-net in base 27, using
- base change [i] based on digital (4, 48, 154)-net over F81, using
- net from sequence [i] based on digital (4, 153)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 154, using
- net from sequence [i] based on digital (4, 153)-sequence over F81, using
(64−44, 64, 5068)-Net in Base 27 — Upper bound on s
There is no (20, 64, 5069)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 40 577837 393478 916001 732623 760361 485499 128192 770895 681663 854042 000339 229882 023065 797346 775233 > 2764 [i]