Best Known (106−45, 106, s)-Nets in Base 5
(106−45, 106, 132)-Net over F5 — Constructive and digital
Digital (61, 106, 132)-net over F5, using
- 8 times m-reduction [i] based on digital (61, 114, 132)-net over F5, using
- trace code for nets [i] based on digital (4, 57, 66)-net over F25, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 4 and N(F) ≥ 66, using
- net from sequence [i] based on digital (4, 65)-sequence over F25, using
- trace code for nets [i] based on digital (4, 57, 66)-net over F25, using
(106−45, 106, 194)-Net over F5 — Digital
Digital (61, 106, 194)-net over F5, using
(106−45, 106, 4890)-Net in Base 5 — Upper bound on s
There is no (61, 106, 4891)-net in base 5, because
- 1 times m-reduction [i] would yield (61, 105, 4891)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 24 687091 146030 103245 650813 019794 294757 474843 482033 380231 423431 074625 011625 > 5105 [i]