MinT - Best Known (24−19, 24, s)-Nets in Base 64

Best Known (24−19, 24, s)-Nets in Base 64

(24−19, 24, 128)-Net over F₆₄ — Constructive and digital

Digital (5, 24, 128)-net over F₆₄, using

net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
  - a function field by SÃ©mirat [i]

(24−19, 24, 133)-Net over F₆₄ — Digital

Digital (5, 24, 133)-net over F₆₄, using

net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
  - a curve from the manYPoints database [i]

(24−19, 24, 150)-Net in Base 64 — Constructive

(5, 24, 150)-net in base 64, using

4 times m-reduction [i] based on (5, 28, 150)-net in base 64, using
- base change [i] based on digital (1, 24, 150)-net over F₁₂₈, using
  - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(24−19, 24, 2713)-Net in Base 64 — Upper bound on s

There is no (5, 24, 2714)-net in base 64, because

1 times m-reduction [i] would yield (5, 23, 2714)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 348939 669521 239441 888453 478227 098574 699825 > 64²³ [i]