MinT - Best Known (191, 191+55, s)-Nets in Base 2

Best Known (191, 191+55, s)-Nets in Base 2

(191, 191+55, 260)-Net over F₂ — Constructive and digital

Digital (191, 246, 260)-net over F₂, using

2² 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]

(191, 191+55, 448)-Net over F₂ — Digital

Digital (191, 246, 448)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(191, 191+55, 5848)-Net in Base 2 — Upper bound on s

There is no (191, 246, 5849)-net in base 2, because

1 times m-reduction [i] would yield (191, 245, 5849)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 56 740421 224125 144659 771566 628949 414696 338939 550586 644699 628055 566025 572040 > 2²⁴⁵ [i]