Best Known (120−49, 120, s)-Nets in Base 5
(120−49, 120, 252)-Net over F5 — Constructive and digital
Digital (71, 120, 252)-net over F5, using
- 2 times m-reduction [i] based on digital (71, 122, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 61, 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, 61, 126)-net over F25, using
(120−49, 120, 7144)-Net in Base 5 — Upper bound on s
There is no (71, 120, 7145)-net in base 5, because
- 1 times m-reduction [i] would yield (71, 119, 7145)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 150751 970137 076775 464957 463381 283091 195792 850334 504107 718554 466344 071571 280536 785825 > 5119 [i]