MinT - Best Known (145, 145+38, s)-Nets in Base 2

Best Known (145, 145+38, s)-Nets in Base 2

(145, 145+38, 260)-Net over F₂ — Constructive and digital

Digital (145, 183, 260)-net over F₂, using

t-expansion [i] based on 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]

(145, 145+38, 432)-Net over F₂ — Digital

Digital (145, 183, 432)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(145, 145+38, 6261)-Net in Base 2 — Upper bound on s

There is no (145, 183, 6262)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12 279858 891100 323362 116067 090829 066793 080155 801421 372374 > 2¹⁸³ [i]