MinT - Best Known (197−39, 197, s)-Nets in Base 2

Best Known (197−39, 197, s)-Nets in Base 2

(197−39, 197, 260)-Net over F₂ — Constructive and digital

Digital (158, 197, 260)-net over F₂, using

t-expansion [i] based on digital (156, 197, 260)-net over F₂, using
- 3 times m-reduction [i] based on digital (156, 200, 260)-net over F₂, using
  - trace code for nets [i] based on digital (6, 50, 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]

(197−39, 197, 531)-Net over F₂ — Digital

Digital (158, 197, 531)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−39, 197, 10077)-Net in Base 2 — Upper bound on s

There is no (158, 197, 10078)-net in base 2, because

1 times m-reduction [i] would yield (158, 196, 10078)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 100434 556387 947366 690956 324176 820107 942031 922154 554766 793882 > 2¹⁹⁶ [i]