MinT - Best Known (86−48, 86, s)-Nets in Base 64

Best Known (86−48, 86, s)-Nets in Base 64

(86−48, 86, 513)-Net over F₆₄ — Constructive and digital

Digital (38, 86, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 86, 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]

(86−48, 86, 602)-Net over F₆₄ — Digital

Digital (38, 86, 602)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−48, 86, 461483)-Net in Base 64 — Upper bound on s

There is no (38, 86, 461484)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 214533 646222 333589 798098 919787 538303 154151 093152 995137 824131 811833 791248 468330 796340 282739 873418 903998 844531 118269 464164 696967 682841 809051 221761 989747 774706 > 64⁸⁶ [i]