Best Known (85−45, 85, s)-Nets in Base 27
(85−45, 85, 178)-Net over F27 — Constructive and digital
Digital (40, 85, 178)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (8, 30, 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 (10, 55, 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 (8, 30, 84)-net over F27, using
(85−45, 85, 370)-Net in Base 27 — Constructive
(40, 85, 370)-net in base 27, using
- 11 times m-reduction [i] based on (40, 96, 370)-net in base 27, using
- base change [i] based on digital (16, 72, 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, 72, 370)-net over F81, using
(85−45, 85, 388)-Net over F27 — Digital
Digital (40, 85, 388)-net over F27, using
(85−45, 85, 101633)-Net in Base 27 — Upper bound on s
There is no (40, 85, 101634)-net in base 27, because
- 1 times m-reduction [i] would yield (40, 84, 101634)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 1 716216 282933 887008 912538 258216 285023 376815 700865 668663 549050 756477 080778 047779 377887 961601 396185 607372 626992 608718 216477 > 2784 [i]