Best Known (64−45, 64, s)-Nets in Base 27
(64−45, 64, 108)-Net over F27 — Constructive and digital
Digital (19, 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
(64−45, 64, 116)-Net in Base 27 — Constructive
(19, 64, 116)-net in base 27, using
- 4 times m-reduction [i] based on (19, 68, 116)-net in base 27, using
- base change [i] based on digital (2, 51, 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, 51, 116)-net over F81, using
(64−45, 64, 148)-Net over F27 — Digital
Digital (19, 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
(64−45, 64, 4361)-Net in Base 27 — Upper bound on s
There is no (19, 64, 4362)-net in base 27, because
- 1 times m-reduction [i] would yield (19, 63, 4362)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 501540 961557 169111 865512 756055 257100 566723 987046 152716 137424 996578 979895 540627 662119 667917 > 2763 [i]