MinT - Best Known (24, 79, s)-Nets in Base 64

Best Known (24, 79, s)-Nets in Base 64

(24, 79, 177)-Net over F₆₄ — Constructive and digital

Digital (24, 79, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 79, 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]

(24, 79, 288)-Net in Base 64 — Constructive

(24, 79, 288)-net in base 64, using

t-expansion [i] based on (22, 79, 288)-net in base 64, using
- 12 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]

(24, 79, 342)-Net over F₆₄ — Digital

Digital (24, 79, 342)-net over F₆₄, using

t-expansion [i] based on digital (20, 79, 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]

(24, 79, 28623)-Net in Base 64 — Upper bound on s

There is no (24, 79, 28624)-net in base 64, because

1 times m-reduction [i] would yield (24, 78, 28624)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 762 834000 232960 113655 710440 085664 377849 640467 269264 679104 863554 717370 689710 988646 760537 231309 603275 040911 321039 054693 399289 988649 837848 739300 > 64⁷⁸ [i]