MinT - Best Known (252−178, 252, s)-Nets in Base 4

Best Known (252−178, 252, s)-Nets in Base 4

(252−178, 252, 104)-Net over F₄ — Constructive and digital

Digital (74, 252, 104)-net over F₄, using

t-expansion [i] based on digital (73, 252, 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]

(252−178, 252, 112)-Net over F₄ — Digital

Digital (74, 252, 112)-net over F₄, using

t-expansion [i] based on digital (73, 252, 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]

(252−178, 252, 502)-Net in Base 4 — Upper bound on s

There is no (74, 252, 503)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 55 074912 216902 321952 783423 501335 868302 346231 997996 988470 233334 568331 295103 831764 881641 664030 182616 055785 407156 368734 323657 376039 564247 427920 709868 411544 > 4²⁵² [i]