MinT - Best Known (64, 64+54, s)-Nets in Base 4

Best Known (64, 64+54, s)-Nets in Base 4

(64, 64+54, 98)-Net over F₄ — Constructive and digital

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+54, 122)-Net over F₄ — Digital

Digital (64, 118, 122)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+54, 1535)-Net in Base 4 — Upper bound on s

There is no (64, 118, 1536)-net in base 4, because

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]