MinT - Best Known (75−41, 75, s)-Nets in Base 64

Best Known (75−41, 75, s)-Nets in Base 64

(75−41, 75, 513)-Net over F₆₄ — Constructive and digital

Digital (34, 75, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 75, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]

(75−41, 75, 630)-Net over F₆₄ — Digital

Digital (34, 75, 630)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−41, 75, 635074)-Net in Base 64 — Upper bound on s

There is no (34, 75, 635075)-net in base 64, because

1 times m-reduction [i] would yield (34, 74, 635075)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 45 427724 299726 127306 481859 295855 197597 069282 732770 625440 652067 322901 213044 201800 442858 601631 696131 281012 878362 400041 529605 468786 660336 > 64⁷⁴ [i]