MinT - Best Known (35−27, 35, s)-Nets in Base 64

Best Known (35−27, 35, s)-Nets in Base 64

(35−27, 35, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 35, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 35, 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]

(35−27, 35, 192)-Net in Base 64 — Constructive

(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]

(35−27, 35, 4757)-Net in Base 64 — Upper bound on s

There is no (8, 35, 4758)-net in base 64, because

1 times m-reduction [i] would yield (8, 34, 4758)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 25 764522 555197 963650 417405 978561 100727 043469 075147 171711 633230 > 64³⁴ [i]