Best Known (74, 74+52, s)-Nets in Base 5
(74, 74+52, 252)-Net over F5 — Constructive and digital
Digital (74, 126, 252)-net over F5, using
- 2 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
(74, 74+52, 6416)-Net in Base 5 — Upper bound on s
There is no (74, 126, 6417)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 11801 096653 671141 932284 010317 518477 239269 147429 347827 874510 688727 524834 782220 470481 568441 > 5126 [i]