MinT - Best Known (86−25, 86, s)-Nets in Base 4

Best Known (86−25, 86, s)-Nets in Base 4

(86−25, 86, 312)-Net over F₄ — Constructive and digital

Digital (61, 86, 312)-net over F₄, using

1 times m-reduction [i] based on digital (61, 87, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 29, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(86−25, 86, 481)-Net over F₄ — Digital

Digital (61, 86, 481)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−25, 86, 32411)-Net in Base 4 — Upper bound on s

There is no (61, 86, 32412)-net in base 4, because

1 times m-reduction [i] would yield (61, 85, 32412)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1496 632473 018504 235625 187584 668750 054185 171403 428580 > 4⁸⁵ [i]