MinT - Best Known (252−86, 252, s)-Nets in Base 2

Best Known (252−86, 252, s)-Nets in Base 2

(252−86, 252, 112)-Net over F₂ — Constructive and digital

Digital (166, 252, 112)-net over F₂, using

t-expansion [i] based on digital (163, 252, 112)-net over F₂, using
- 8 times m-reduction [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]

(252−86, 252, 161)-Net over F₂ — Digital

Digital (166, 252, 161)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−86, 252, 918)-Net in Base 2 — Upper bound on s

There is no (166, 252, 919)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7303 520385 720784 360705 812634 223586 887394 358769 704853 932491 623721 247386 106992 > 2²⁵² [i]