MinT - Best Known (225−74, 225, s)-Nets in Base 2

Best Known (225−74, 225, s)-Nets in Base 2

(225−74, 225, 112)-Net over F₂ — Constructive and digital

Digital (151, 225, 112)-net over F₂, using

11 times m-reduction [i] based on digital (151, 236, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 118, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(225−74, 225, 159)-Net over F₂ — Digital

Digital (151, 225, 159)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−74, 225, 938)-Net in Base 2 — Upper bound on s

There is no (151, 225, 939)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 55 290167 135959 832626 731776 752679 409879 050297 769868 015232 449686 090048 > 2²²⁵ [i]