MinT - Best Known (8, 8+25, s)-Nets in Base 64

Best Known (8, 8+25, s)-Nets in Base 64

(8, 8+25, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 33, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 33, 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]

(8, 8+25, 192)-Net in Base 64 — Constructive

(8, 33, 192)-net in base 64, using

2 times m-reduction [i] based on (8, 35, 192)-net in base 64, using
- base change [i] based on digital (3, 30, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(8, 8+25, 5496)-Net in Base 64 — Upper bound on s

There is no (8, 33, 5497)-net in base 64, because

1 times m-reduction [i] would yield (8, 32, 5497)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 6289 982488 974287 478184 449774 810980 334979 814739 298016 243380 > 64³² [i]