MinT - Best Known (64, 64+53, s)-Nets in Base 4

Best Known (64, 64+53, s)-Nets in Base 4

(64, 64+53, 98)-Net over F₄ — Constructive and digital

Digital (64, 117, 98)-net over F₄, using

1 times m-reduction [i] based on digital (64, 118, 98)-net over F₄, using
- trace code for nets [i] based on digital (5, 59, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(64, 64+53, 125)-Net over F₄ — Digital

Digital (64, 117, 125)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+53, 1686)-Net in Base 4 — Upper bound on s

There is no (64, 117, 1687)-net in base 4, because

1 times m-reduction [i] would yield (64, 116, 1687)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 6992 884258 548714 729521 330734 933339 375513 044930 252743 753499 798647 076880 > 4¹¹⁶ [i]