MinT - Best Known (144, 144+64, s)-Nets in Base 2

Best Known (144, 144+64, s)-Nets in Base 2

(144, 144+64, 112)-Net over F₂ — Constructive and digital

Digital (144, 208, 112)-net over F₂, using

14 times m-reduction [i] based on digital (144, 222, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 111, 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]

(144, 144+64, 174)-Net over F₂ — Digital

Digital (144, 208, 174)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+64, 1111)-Net in Base 2 — Upper bound on s

There is no (144, 208, 1112)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 422 708212 663496 683197 651906 274718 529498 075403 477941 993888 981762 > 2²⁰⁸ [i]