Best Known (84, 84+58, s)-Nets in Base 5
(84, 84+58, 252)-Net over F5 — Constructive and digital
Digital (84, 142, 252)-net over F5, using
- 6 times m-reduction [i] based on digital (84, 148, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 74, 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, 74, 126)-net over F25, using
(84, 84+58, 283)-Net over F5 — Digital
Digital (84, 142, 283)-net over F5, using
(84, 84+58, 7698)-Net in Base 5 — Upper bound on s
There is no (84, 142, 7699)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1796 703139 045388 220941 280189 884897 814239 782704 740838 103213 358469 785285 043080 483418 254746 859499 082205 > 5142 [i]