Best Known (124−50, 124, s)-Nets in Base 5
(124−50, 124, 252)-Net over F5 — Constructive and digital
Digital (74, 124, 252)-net over F5, using
- 4 times m-reduction [i] based on digital (74, 128, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 64, 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, 64, 126)-net over F25, using
(124−50, 124, 264)-Net over F5 — Digital
Digital (74, 124, 264)-net over F5, using
(124−50, 124, 7436)-Net in Base 5 — Upper bound on s
There is no (74, 124, 7437)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 470 311962 539645 217610 664973 188538 047474 084965 695475 899644 158987 148476 149943 031899 952213 > 5124 [i]