Best Known (89, 146, s)-Nets in Base 5
(89, 146, 252)-Net over F5 — Constructive and digital
Digital (89, 146, 252)-net over F5, using
- t-expansion [i] based on digital (85, 146, 252)-net over F5, using
- 4 times m-reduction [i] based on digital (85, 150, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 75, 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, 75, 126)-net over F25, using
- 4 times m-reduction [i] based on digital (85, 150, 252)-net over F5, using
(89, 146, 341)-Net over F5 — Digital
Digital (89, 146, 341)-net over F5, using
(89, 146, 11745)-Net in Base 5 — Upper bound on s
There is no (89, 146, 11746)-net in base 5, because
- 1 times m-reduction [i] would yield (89, 145, 11746)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 224724 323555 932149 331515 588210 058889 666952 794701 741276 320684 878687 176021 950578 419668 673180 707779 707585 > 5145 [i]