Best Known (135−55, 135, s)-Nets in Base 5
(135−55, 135, 252)-Net over F5 — Constructive and digital
Digital (80, 135, 252)-net over F5, using
- 5 times m-reduction [i] based on digital (80, 140, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 70, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 70, 126)-net over F25, using
(135−55, 135, 274)-Net over F5 — Digital
Digital (80, 135, 274)-net over F5, using
(135−55, 135, 8021)-Net in Base 5 — Upper bound on s
There is no (80, 135, 8022)-net in base 5, because
- 1 times m-reduction [i] would yield (80, 134, 8022)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 4603 381264 376542 394382 518679 186500 085322 894114 350323 622081 250360 807331 273467 603127 602207 957625 > 5134 [i]