MinT - Best Known (220−74, 220, s)-Nets in Base 2

Best Known (220−74, 220, s)-Nets in Base 2

(220−74, 220, 112)-Net over F₂ — Constructive and digital

Digital (146, 220, 112)-net over F₂, using

6 times m-reduction [i] based on digital (146, 226, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 113, 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]

(220−74, 220, 148)-Net over F₂ — Digital

Digital (146, 220, 148)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−74, 220, 849)-Net in Base 2 — Upper bound on s

There is no (146, 220, 850)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 701758 422369 395555 963256 565012 798086 935867 884204 930233 507541 812440 > 2²²⁰ [i]