MinT - Best Known (239−80, 239, s)-Nets in Base 2

Best Known (239−80, 239, s)-Nets in Base 2

(239−80, 239, 112)-Net over F₂ — Constructive and digital

Digital (159, 239, 112)-net over F₂, using

13 times m-reduction [i] based on digital (159, 252, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 126, 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]

(239−80, 239, 161)-Net over F₂ — Digital

Digital (159, 239, 161)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−80, 239, 933)-Net in Base 2 — Upper bound on s

There is no (159, 239, 934)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 885863 374975 707275 318951 420307 175519 523586 568128 049521 050820 395010 972240 > 2²³⁹ [i]