Best Known (73−52, 73, s)-Nets in Base 27
(73−52, 73, 108)-Net over F27 — Constructive and digital
Digital (21, 73, 108)-net over F27, using
- t-expansion [i] based on digital (18, 73, 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
(73−52, 73, 116)-Net in Base 27 — Constructive
(21, 73, 116)-net in base 27, using
- 3 times m-reduction [i] based on (21, 76, 116)-net in base 27, using
- base change [i] based on digital (2, 57, 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, 57, 116)-net over F81, using
(73−52, 73, 163)-Net over F27 — Digital
Digital (21, 73, 163)-net over F27, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 21 and N(F) ≥ 163, using
(73−52, 73, 4224)-Net in Base 27 — Upper bound on s
There is no (21, 73, 4225)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 309 869673 875070 203011 636485 798885 767576 790976 652965 588149 525244 118499 599948 494572 620240 245483 655393 594745 > 2773 [i]