MinT - Best Known (90−47, 90, s)-Nets in Base 64

Best Known (90−47, 90, s)-Nets in Base 64

(90−47, 90, 513)-Net over F₆₄ — Constructive and digital

Digital (43, 90, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 90, 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]

(90−47, 90, 1000)-Net over F₆₄ — Digital

Digital (43, 90, 1000)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−47, 90, 1459632)-Net in Base 64 — Upper bound on s

There is no (43, 90, 1459633)-net in base 64, because

1 times m-reduction [i] would yield (43, 89, 1459633)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 56236 783713 369620 055807 042980 261730 540239 035056 988794 017099 850611 348217 786297 635495 854245 569257 852354 126173 975439 471681 713312 524094 763737 641209 360253 408193 172960 > 64⁸⁹ [i]