MinT - Best Known (225−142, 225, s)-Nets in Base 4

Best Known (225−142, 225, s)-Nets in Base 4

(225−142, 225, 104)-Net over F₄ — Constructive and digital

Digital (83, 225, 104)-net over F₄, using

t-expansion [i] based on digital (73, 225, 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]

(225−142, 225, 129)-Net over F₄ — Digital

Digital (83, 225, 129)-net over F₄, using

t-expansion [i] based on digital (81, 225, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(225−142, 225, 678)-Net in Base 4 — Upper bound on s

There is no (83, 225, 679)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3106 789216 261955 446875 887624 823256 134129 241064 019900 004525 820090 635192 336640 347816 664695 095072 642649 452090 964427 529384 734039 440382 708824 > 4²²⁵ [i]