MinT - Best Known (74, 74+78, s)-Nets in Base 4

Best Known (74, 74+78, s)-Nets in Base 4

(74, 74+78, 104)-Net over F₄ — Constructive and digital

Digital (74, 152, 104)-net over F₄, using

t-expansion [i] based on digital (73, 152, 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+78, 112)-Net over F₄ — Digital

Digital (74, 152, 112)-net over F₄, using

t-expansion [i] based on digital (73, 152, 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+78, 1108)-Net in Base 4 — Upper bound on s

There is no (74, 152, 1109)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 33 670406 531802 162573 162953 400096 090500 022144 533604 422168 510499 400776 961692 118054 344552 350560 > 4¹⁵² [i]