Best Known (74−42, 74, s)-Nets in Base 27
(74−42, 74, 146)-Net over F27 — Constructive and digital
Digital (32, 74, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 25, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (7, 49, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 25, 64)-net over F27, using
(74−42, 74, 224)-Net in Base 27 — Constructive
(32, 74, 224)-net in base 27, using
- 2 times m-reduction [i] based on (32, 76, 224)-net in base 27, using
- base change [i] based on digital (13, 57, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 57, 224)-net over F81, using
(74−42, 74, 233)-Net over F27 — Digital
Digital (32, 74, 233)-net over F27, using
(74−42, 74, 298)-Net in Base 27
(32, 74, 298)-net in base 27, using
- 6 times m-reduction [i] based on (32, 80, 298)-net in base 27, using
- base change [i] based on digital (12, 60, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 60, 298)-net over F81, using
(74−42, 74, 36918)-Net in Base 27 — Upper bound on s
There is no (32, 74, 36919)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 8337 084160 300803 219487 443002 866389 566200 040934 922313 125645 070652 607383 044166 361287 579002 722636 652689 558095 > 2774 [i]