MinT - Best Known (144, 144+39, s)-Nets in Base 2

Best Known (144, 144+39, s)-Nets in Base 2

(144, 144+39, 260)-Net over F₂ — Constructive and digital

Digital (144, 183, 260)-net over F₂, using

1 times m-reduction [i] based on digital (144, 184, 260)-net over F₂, using
- trace code for nets [i] based on digital (6, 46, 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]

(144, 144+39, 400)-Net over F₂ — Digital

Digital (144, 183, 400)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+39, 6036)-Net in Base 2 — Upper bound on s

There is no (144, 183, 6037)-net in base 2, because

1 times m-reduction [i] would yield (144, 182, 6037)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 6 146258 286073 978304 508437 088009 084340 073054 237627 736544 > 2¹⁸² [i]