MinT - Best Known (64, 64+49, s)-Nets in Base 5

Best Known (64, 64+49, s)-Nets in Base 5

(64, 64+49, 132)-Net over F₅ — Constructive and digital

Digital (64, 113, 132)-net over F₅, using

7 times m-reduction [i] based on digital (64, 120, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 60, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(64, 64+49, 189)-Net over F₅ — Digital

Digital (64, 113, 189)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+49, 4461)-Net in Base 5 — Upper bound on s

There is no (64, 113, 4462)-net in base 5, because

1 times m-reduction [i] would yield (64, 112, 4462)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 932795 769476 555535 194900 992670 016022 843186 973546 774152 368309 565543 315810 308225 > 5¹¹² [i]