Best Known (124−52, 124, s)-Nets in Base 5
(124−52, 124, 252)-Net over F5 — Constructive and digital
Digital (72, 124, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 62, 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
(124−52, 124, 5666)-Net in Base 5 — Upper bound on s
There is no (72, 124, 5667)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 470 840451 139487 823412 290874 103197 229920 396450 501400 135007 195337 897394 728731 879556 270361 > 5124 [i]