MinT - Best Known (40, 40+50, s)-Nets in Base 64

Best Known (40, 40+50, s)-Nets in Base 64

(40, 40+50, 513)-Net over F₆₄ — Constructive and digital

Digital (40, 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]

(40, 40+50, 644)-Net over F₆₄ — Digital

Digital (40, 90, 644)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+50, 513479)-Net in Base 64 — Upper bound on s

There is no (40, 90, 513480)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 599303 701780 483193 513009 338642 188337 378807 046904 930541 325927 564882 509539 626003 274527 395763 778550 504081 242381 722278 186885 250977 740480 370013 285943 467481 410101 532776 > 64⁹⁰ [i]