MinT - Best Known (260−86, 260, s)-Nets in Base 2

Best Known (260−86, 260, s)-Nets in Base 2

(260−86, 260, 112)-Net over F₂ — Constructive and digital

Digital (174, 260, 112)-net over F₂, using

t-expansion [i] based on digital (163, 260, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 130, 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]

(260−86, 260, 178)-Net over F₂ — Digital

Digital (174, 260, 178)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(260−86, 260, 1053)-Net in Base 2 — Upper bound on s

There is no (174, 260, 1054)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 881890 427691 680907 127782 433862 414256 433983 935797 698820 464009 565056 607442 134336 > 2²⁶⁰ [i]