Best Known (61−42, 61, s)-Nets in Base 27
(61−42, 61, 108)-Net over F27 — Constructive and digital
Digital (19, 61, 108)-net over F27, using
- t-expansion [i] based on digital (18, 61, 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
(61−42, 61, 116)-Net in Base 27 — Constructive
(19, 61, 116)-net in base 27, using
- 7 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
(61−42, 61, 148)-Net over F27 — Digital
Digital (19, 61, 148)-net over F27, using
- t-expansion [i] based on digital (18, 61, 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
(61−42, 61, 4789)-Net in Base 27 — Upper bound on s
There is no (19, 61, 4790)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2059 142151 745307 366799 954816 684360 283977 568222 676076 957185 154106 154292 698542 824368 313909 > 2761 [i]