MinT - Best Known (37, 37+47, s)-Nets in Base 64

Best Known (37, 37+47, s)-Nets in Base 64

(37, 37+47, 513)-Net over F₆₄ — Constructive and digital

Digital (37, 84, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 84, 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]

(37, 37+47, 581)-Net over F₆₄ — Digital

Digital (37, 84, 581)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(37, 37+47, 493241)-Net in Base 64 — Upper bound on s

There is no (37, 84, 493242)-net in base 64, because

1 times m-reduction [i] would yield (37, 83, 493242)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 818369 648391 971171 923476 076144 270636 513900 356820 941472 562737 646996 621589 630263 673245 412647 848133 427241 641114 528140 748921 590510 923087 055650 302921 611452 > 64⁸³ [i]