Best Known (54, 88, s)-Nets in Base 5
(54, 88, 252)-Net over F5 — Constructive and digital
Digital (54, 88, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 44, 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
(54, 88, 7436)-Net in Base 5 — Upper bound on s
There is no (54, 88, 7437)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 32 348744 937465 452978 637393 884741 541551 490548 968885 782882 235125 > 588 [i]