MinT - Best Known (193, 193+51, s)-Nets in Base 2

Best Known (193, 193+51, s)-Nets in Base 2

(193, 193+51, 260)-Net over F₂ — Constructive and digital

Digital (193, 244, 260)-net over F₂, using

t-expansion [i] based on digital (192, 244, 260)-net over F₂, using
- 4 times m-reduction [i] based on digital (192, 248, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 62, 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]

(193, 193+51, 537)-Net over F₂ — Digital

Digital (193, 244, 537)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(193, 193+51, 8546)-Net in Base 2 — Upper bound on s

There is no (193, 244, 8547)-net in base 2, because

1 times m-reduction [i] would yield (193, 243, 8547)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14 174411 602356 652510 247872 423138 296721 980334 645298 758535 471233 763653 069168 > 2²⁴³ [i]