Best Known (90−49, 90, s)-Nets in Base 27
(90−49, 90, 176)-Net over F27 — Constructive and digital
Digital (41, 90, 176)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 31, 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, 59, 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, 31, 82)-net over F27, using
(90−49, 90, 344)-Net over F27 — Digital
Digital (41, 90, 344)-net over F27, using
(90−49, 90, 370)-Net in Base 27 — Constructive
(41, 90, 370)-net in base 27, using
- 10 times m-reduction [i] based on (41, 100, 370)-net in base 27, using
- base change [i] based on digital (16, 75, 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, 75, 370)-net over F81, using
(90−49, 90, 76611)-Net in Base 27 — Upper bound on s
There is no (41, 90, 76612)-net in base 27, because
- 1 times m-reduction [i] would yield (41, 89, 76612)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 24 630194 549719 615667 330624 776019 296035 750965 246842 911538 116399 712350 612484 164638 134420 476611 655805 783097 141412 022454 565964 122177 > 2789 [i]