Best Known (94−56, 94, s)-Nets in Base 27
(94−56, 94, 140)-Net over F27 — Constructive and digital
Digital (38, 94, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 32, 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 (6, 62, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (4, 32, 64)-net over F27, using
(94−56, 94, 224)-Net in Base 27 — Constructive
(38, 94, 224)-net in base 27, using
- 6 times m-reduction [i] based on (38, 100, 224)-net in base 27, using
- base change [i] based on digital (13, 75, 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, 75, 224)-net over F81, using
(94−56, 94, 244)-Net over F27 — Digital
Digital (38, 94, 244)-net over F27, using
- t-expansion [i] based on digital (36, 94, 244)-net over F27, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 36 and N(F) ≥ 244, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
(94−56, 94, 298)-Net in Base 27
(38, 94, 298)-net in base 27, using
- 10 times m-reduction [i] based on (38, 104, 298)-net in base 27, using
- base change [i] based on digital (12, 78, 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, 78, 298)-net over F81, using
(94−56, 94, 27739)-Net in Base 27 — Upper bound on s
There is no (38, 94, 27740)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 353 574789 103418 438881 252377 846792 616285 966832 728169 604386 227488 555103 132050 526890 128010 861819 329156 367752 087497 517251 844754 770457 923521 > 2794 [i]