MinT - Best Known (197−42, 197, s)-Nets in Base 2

Best Known (197−42, 197, s)-Nets in Base 2

(197−42, 197, 260)-Net over F₂ — Constructive and digital

Digital (155, 197, 260)-net over F₂, using

2¹ times duplication [i] based on digital (154, 196, 260)-net over F₂, using
- t-expansion [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]

(197−42, 197, 424)-Net over F₂ — Digital

Digital (155, 197, 424)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−42, 197, 5755)-Net in Base 2 — Upper bound on s

There is no (155, 197, 5756)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 200937 140517 891089 979809 806679 782290 020539 348909 415276 251746 > 2¹⁹⁷ [i]