MinT - Best Known (50, 50+29, s)-Nets in Base 5

Best Known (50, 50+29, s)-Nets in Base 5

(50, 50+29, 252)-Net over F₅ — Constructive and digital

Digital (50, 79, 252)-net over F₅, using

1 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+29, 270)-Net over F₅ — Digital

Digital (50, 79, 270)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+29, 11838)-Net in Base 5 — Upper bound on s

There is no (50, 79, 11839)-net in base 5, because

1 times m-reduction [i] would yield (50, 78, 11839)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 311110 972340 859567 334516 130436 890511 809770 936150 312905 > 5⁷⁸ [i]