MinT - Best Known (41, 41+47, s)-Nets in Base 64

Best Known (41, 41+47, s)-Nets in Base 64

(41, 41+47, 513)-Net over F₆₄ — Constructive and digital

Digital (41, 88, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 88, 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]

(41, 41+47, 838)-Net over F₆₄ — Digital

Digital (41, 88, 838)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(41, 41+47, 1016676)-Net in Base 64 — Upper bound on s

There is no (41, 88, 1016677)-net in base 64, because

1 times m-reduction [i] would yield (41, 87, 1016677)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 13 729630 211467 751208 488674 520285 723844 782420 665541 893495 136449 188495 289901 039806 397165 673900 198511 465727 364048 147683 880496 688382 626549 852278 945280 033753 026528 > 64⁸⁷ [i]