MinT - Best Known (190, 190+55, s)-Nets in Base 2

Best Known (190, 190+55, s)-Nets in Base 2

(190, 190+55, 260)-Net over F₂ — Constructive and digital

Digital (190, 245, 260)-net over F₂, using

2¹ times duplication [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]

(190, 190+55, 442)-Net over F₂ — Digital

Digital (190, 245, 442)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(190, 190+55, 5698)-Net in Base 2 — Upper bound on s

There is no (190, 245, 5699)-net in base 2, because

1 times m-reduction [i] would yield (190, 244, 5699)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28 270638 921281 149708 641875 352280 050406 175878 488217 625136 845145 180466 501296 > 2²⁴⁴ [i]