MinT - Best Known (50, 50+27, s)-Nets in Base 5

Best Known (50, 50+27, s)-Nets in Base 5

(50, 50+27, 252)-Net over F₅ — Constructive and digital

Digital (50, 77, 252)-net over F₅, using

3 times m-reduction [i] based on digital (50, 80, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 40, 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]

(50, 50+27, 323)-Net over F₅ — Digital

Digital (50, 77, 323)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+27, 17274)-Net in Base 5 — Upper bound on s

There is no (50, 77, 17275)-net in base 5, because

1 times m-reduction [i] would yield (50, 76, 17275)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 132420 733579 261814 276824 387743 905660 367063 007600 373181 > 5⁷⁶ [i]