MinT - Best Known (39, 86, s)-Nets in Base 64

Best Known (39, 86, s)-Nets in Base 64

(39, 86, 513)-Net over F₆₄ — Constructive and digital

Digital (39, 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]

(39, 86, 702)-Net over F₆₄ — Digital

Digital (39, 86, 702)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 86, 708144)-Net in Base 64 — Upper bound on s

There is no (39, 86, 708145)-net in base 64, because

1 times m-reduction [i] would yield (39, 85, 708145)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3352 038194 794247 951003 907475 081106 658659 738219 686676 681373 739835 881593 924018 420493 824263 299710 198313 642071 250337 566417 210168 232540 038262 374657 476052 469344 > 64⁸⁵ [i]