Best Known (80−42, 80, s)-Nets in Base 27
(80−42, 80, 176)-Net over F27 — Constructive and digital
Digital (38, 80, 176)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 28, 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 (10, 52, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (7, 28, 82)-net over F27, using
(80−42, 80, 370)-Net in Base 27 — Constructive
(38, 80, 370)-net in base 27, using
- 8 times m-reduction [i] based on (38, 88, 370)-net in base 27, using
- base change [i] based on digital (16, 66, 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, 66, 370)-net over F81, using
(80−42, 80, 390)-Net over F27 — Digital
Digital (38, 80, 390)-net over F27, using
(80−42, 80, 94685)-Net in Base 27 — Upper bound on s
There is no (38, 80, 94686)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3 229523 758918 002637 067697 065118 010340 717185 055092 386229 336574 528432 107197 643115 814477 954151 697416 795391 989103 482373 > 2780 [i]