MinT - Best Known (193−38, 193, s)-Nets in Base 2

Best Known (193−38, 193, s)-Nets in Base 2

(193−38, 193, 260)-Net over F₂ — Constructive and digital

Digital (155, 193, 260)-net over F₂, using

t-expansion [i] based on digital (153, 193, 260)-net over F₂, using
- 3 times m-reduction [i] based on digital (153, 196, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 49, 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]

(193−38, 193, 531)-Net over F₂ — Digital

Digital (155, 193, 531)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−38, 193, 9030)-Net in Base 2 — Upper bound on s

There is no (155, 193, 9031)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12571 713651 093031 318776 393122 105139 530470 795755 633975 362440 > 2¹⁹³ [i]