Best Known (144−62, 144, s)-Nets in Base 5
(144−62, 144, 252)-Net over F5 — Constructive and digital
Digital (82, 144, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 72, 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
(144−62, 144, 5457)-Net in Base 5 — Upper bound on s
There is no (82, 144, 5458)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 44956 743581 036093 297368 422647 617847 192465 471897 178870 752229 751710 239540 812335 403914 654697 324485 698409 > 5144 [i]