MinT - Best Known (41, 41+50, s)-Nets in Base 64

Best Known (41, 41+50, s)-Nets in Base 64

(41, 41+50, 513)-Net over F₆₄ — Constructive and digital

Digital (41, 91, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 91, 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+50, 704)-Net over F₆₄ — Digital

Digital (41, 91, 704)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(41, 41+50, 606417)-Net in Base 64 — Upper bound on s

There is no (41, 91, 606418)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 230 352060 931794 992203 389258 749179 044768 713302 231381 200534 795603 609899 170873 650559 968296 128574 857745 529854 698173 577951 160373 304176 002660 063648 471336 575435 496928 805192 > 64⁹¹ [i]