MinT - Best Known (73−49, 73, s)-Nets in Base 64

Best Known (73−49, 73, s)-Nets in Base 64

(73−49, 73, 177)-Net over F₆₄ — Constructive and digital

Digital (24, 73, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 73, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(73−49, 73, 288)-Net in Base 64 — Constructive

(24, 73, 288)-net in base 64, using

t-expansion [i] based on (22, 73, 288)-net in base 64, using
- 18 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
  - base change [i] based on digital (9, 78, 288)-net over F₁₂₈, using
    - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(73−49, 73, 342)-Net over F₆₄ — Digital

Digital (24, 73, 342)-net over F₆₄, using

t-expansion [i] based on digital (20, 73, 342)-net over F₆₄, using
- net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
    - a curve from the manYPoints database [i]

(73−49, 73, 40778)-Net in Base 64 — Upper bound on s

There is no (24, 73, 40779)-net in base 64, because

1 times m-reduction [i] would yield (24, 72, 40779)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 11091 272452 435961 222099 159422 101071 850590 078993 381831 285054 085138 515443 848533 957720 617323 476206 149477 944347 420750 173645 996660 636484 > 64⁷² [i]