MinT - Best Known (119−55, 119, s)-Nets in Base 4

Best Known (119−55, 119, s)-Nets in Base 4

(119−55, 119, 90)-Net over F₄ — Constructive and digital

Digital (64, 119, 90)-net over F₄, using

1 times m-reduction [i] based on digital (64, 120, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 60, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(119−55, 119, 119)-Net over F₄ — Digital

Digital (64, 119, 119)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−55, 119, 1535)-Net in Base 4 — Upper bound on s

There is no (64, 119, 1536)-net in base 4, because

1 times m-reduction [i] would yield (64, 118, 1536)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 110590 731036 082321 156074 728852 356864 735091 121909 200168 341966 252573 955617 > 4¹¹⁸ [i]