Best Known (42, 42+54, s)-Nets in Base 27
(42, 42+54, 166)-Net over F27 — Constructive and digital
Digital (42, 96, 166)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 34, 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 (8, 62, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (7, 34, 82)-net over F27, using
(42, 42+54, 301)-Net over F27 — Digital
Digital (42, 96, 301)-net over F27, using
(42, 42+54, 370)-Net in Base 27 — Constructive
(42, 96, 370)-net in base 27, using
- 8 times m-reduction [i] based on (42, 104, 370)-net in base 27, using
- base change [i] based on digital (16, 78, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 78, 370)-net over F81, using
(42, 42+54, 51595)-Net in Base 27 — Upper bound on s
There is no (42, 96, 51596)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 257703 515136 497406 851244 615384 511213 915827 956211 936982 051453 190450 678742 002969 863120 761548 161848 758121 175542 212561 609474 235650 304848 228785 > 2796 [i]