MinT - Best Known (74, 74+152, s)-Nets in Base 4

Best Known (74, 74+152, s)-Nets in Base 4

(74, 74+152, 104)-Net over F₄ — Constructive and digital

Digital (74, 226, 104)-net over F₄, using

t-expansion [i] based on digital (73, 226, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(74, 74+152, 112)-Net over F₄ — Digital

Digital (74, 226, 112)-net over F₄, using

t-expansion [i] based on digital (73, 226, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(74, 74+152, 538)-Net in Base 4 — Upper bound on s

There is no (74, 226, 539)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12446 556699 123519 351622 462403 722558 893958 562858 967985 659245 923667 467379 749807 246846 976654 322674 179162 180693 826812 884740 496149 842069 095904 > 4²²⁶ [i]