Best Known (125−46, 125, s)-Nets in Base 5
(125−46, 125, 252)-Net over F5 — Constructive and digital
Digital (79, 125, 252)-net over F5, using
- 13 times m-reduction [i] based on digital (79, 138, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 69, 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, 69, 126)-net over F25, using
(125−46, 125, 377)-Net over F5 — Digital
Digital (79, 125, 377)-net over F5, using
(125−46, 125, 14813)-Net in Base 5 — Upper bound on s
There is no (79, 125, 14814)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 2353 056795 035687 559977 069520 669516 486987 978450 872555 852241 143639 633428 071211 425608 356505 > 5125 [i]