MinT - Best Known (55−49, 55, s)-Nets in Base 64

Best Known (55−49, 55, s)-Nets in Base 64

(55−49, 55, 128)-Net over F₆₄ — Constructive and digital

Digital (6, 55, 128)-net over F₆₄, using

t-expansion [i] based on digital (5, 55, 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]

(55−49, 55, 161)-Net over F₆₄ — Digital

Digital (6, 55, 161)-net over F₆₄, using

net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
  - a curve from the manYPoints database [i]

(55−49, 55, 1790)-Net in Base 64 — Upper bound on s

There is no (6, 55, 1791)-net in base 64, because

1 times m-reduction [i] would yield (6, 54, 1791)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 34 244094 357027 974415 358196 260617 893376 379025 475484 664339 912971 506312 906513 804484 694007 442734 335209 > 64⁵⁴ [i]