MinT - Best Known (8, 67, s)-Nets in Base 64

Best Known (8, 67, s)-Nets in Base 64

(8, 67, 177)-Net over F₆₄ — Constructive and digital

Digital (8, 67, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 67, 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, 67, 2375)-Net in Base 64 — Upper bound on s

There is no (8, 67, 2376)-net in base 64, because

1 times m-reduction [i] would yield (8, 66, 2376)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 162259 531823 945392 901676 532164 790874 360932 526452 245147 148748 897077 878909 945504 368244 286978 378099 190432 264998 639828 099144 > 64⁶⁶ [i]