Best Known (122−50, 122, s)-Nets in Base 5
(122−50, 122, 252)-Net over F5 — Constructive and digital
Digital (72, 122, 252)-net over F5, using
- 2 times m-reduction [i] based on digital (72, 124, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 62, 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, 62, 126)-net over F25, using
(122−50, 122, 6536)-Net in Base 5 — Upper bound on s
There is no (72, 122, 6537)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 18 860594 104507 081559 863576 377106 190299 089338 268564 553832 519568 822201 440901 455070 092869 > 5122 [i]