MinT - Best Known (45, 45+25, s)-Nets in Base 5

Best Known (45, 45+25, s)-Nets in Base 5

(45, 45+25, 252)-Net over F₅ — Constructive and digital

Digital (45, 70, 252)-net over F₅, using

trace code for nets [i] based on digital (10, 35, 126)-net over F₂₅, using
- net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(45, 45+25, 280)-Net over F₅ — Digital

Digital (45, 70, 280)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+25, 13807)-Net in Base 5 — Upper bound on s

There is no (45, 70, 13808)-net in base 5, because

1 times m-reduction [i] would yield (45, 69, 13808)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 694957 069220 546496 528659 148438 207865 196578 914305 > 5⁶⁹ [i]