MinT - Best Known (39, 87, s)-Nets in Base 64

Best Known (39, 87, s)-Nets in Base 64

(39, 87, 513)-Net over F₆₄ — Constructive and digital

Digital (39, 87, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 87, 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]

(39, 87, 660)-Net over F₆₄ — Digital

Digital (39, 87, 660)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 87, 548801)-Net in Base 64 — Upper bound on s

There is no (39, 87, 548802)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 13 729970 709523 997314 636809 102582 748229 404542 216255 657420 699460 961925 552605 627903 108081 739631 230682 651137 808937 534764 741756 063365 181854 294497 884066 645661 827384 > 64⁸⁷ [i]