Best Known (60, 60+33, s)-Nets in Base 5
(60, 60+33, 252)-Net over F5 — Constructive and digital
Digital (60, 93, 252)-net over F5, using
- 7 times m-reduction [i] based on digital (60, 100, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 50, 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, 50, 126)-net over F25, using
(60, 60+33, 350)-Net over F5 — Digital
Digital (60, 93, 350)-net over F5, using
(60, 60+33, 17753)-Net in Base 5 — Upper bound on s
There is no (60, 93, 17754)-net in base 5, because
- 1 times m-reduction [i] would yield (60, 92, 17754)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 20210 551648 846532 902005 838596 858096 438494 950320 456958 922960 839425 > 592 [i]