Best Known (50, 135, s)-Nets in Base 5
(50, 135, 82)-Net over F5 — Constructive and digital
Digital (50, 135, 82)-net over F5, using
- t-expansion [i] based on digital (48, 135, 82)-net over F5, using
- net from sequence [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- net from sequence [i] based on digital (48, 81)-sequence over F5, using
(50, 135, 96)-Net over F5 — Digital
Digital (50, 135, 96)-net over F5, using
- t-expansion [i] based on digital (49, 135, 96)-net over F5, using
- net from sequence [i] based on digital (49, 95)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 49 and N(F) ≥ 96, using
- net from sequence [i] based on digital (49, 95)-sequence over F5, using
(50, 135, 670)-Net in Base 5 — Upper bound on s
There is no (50, 135, 671)-net in base 5, because
- 1 times m-reduction [i] would yield (50, 134, 671)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 4705 246259 342566 830527 191895 769272 343986 890068 394474 688688 037108 089116 519409 680623 453548 767065 > 5134 [i]