Best Known (53, 53+32, s)-Nets in Base 5
(53, 53+32, 252)-Net over F5 — Constructive and digital
Digital (53, 85, 252)-net over F5, using
- 1 times m-reduction [i] based on digital (53, 86, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 43, 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, 43, 126)-net over F25, using
(53, 53+32, 256)-Net over F5 — Digital
Digital (53, 85, 256)-net over F5, using
(53, 53+32, 8773)-Net in Base 5 — Upper bound on s
There is no (53, 85, 8774)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 258582 819743 590657 773425 793446 114105 972006 191338 556527 838977 > 585 [i]