MinT - Best Known (239−49, 239, s)-Nets in Base 2

Best Known (239−49, 239, s)-Nets in Base 2

(239−49, 239, 260)-Net over F₂ — Constructive and digital

Digital (190, 239, 260)-net over F₂, using

t-expansion [i] based on digital (189, 239, 260)-net over F₂, using
- 5 times m-reduction [i] based on digital (189, 244, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 61, 65)-net over F₁₆, using
    - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(239−49, 239, 558)-Net over F₂ — Digital

Digital (190, 239, 558)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(239−49, 239, 9439)-Net in Base 2 — Upper bound on s

There is no (190, 239, 9440)-net in base 2, because

1 times m-reduction [i] would yield (190, 238, 9440)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 442261 238495 698126 775554 033961 038851 082970 933335 460706 933077 744593 575659 > 2²³⁸ [i]