MinT - Best Known (54, 79, s)-Nets in Base 5

Best Known (54, 79, s)-Nets in Base 5

(54, 79, 252)-Net over F₅ — Constructive and digital

Digital (54, 79, 252)-net over F₅, using

9 times m-reduction [i] based on digital (54, 88, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 44, 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]

(54, 79, 502)-Net over F₅ — Digital

Digital (54, 79, 502)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 79, 46187)-Net in Base 5 — Upper bound on s

There is no (54, 79, 46188)-net in base 5, because

1 times m-reduction [i] would yield (54, 78, 46188)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 308961 738872 686924 472824 754816 361094 225111 536082 952961 > 5⁷⁸ [i]