MinT - Best Known (117, 117+34, s)-Nets in Base 2

Best Known (117, 117+34, s)-Nets in Base 2

(117, 117+34, 195)-Net over F₂ — Constructive and digital

Digital (117, 151, 195)-net over F₂, using

t-expansion [i] based on digital (116, 151, 195)-net over F₂, using
- 2 times m-reduction [i] based on digital (116, 153, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 51, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
        the Suzuki function field over F₈ [i]

(117, 117+34, 293)-Net over F₂ — Digital

Digital (117, 151, 293)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+34, 3361)-Net in Base 2 — Upper bound on s

There is no (117, 151, 3362)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2855 011185 598291 002709 231585 323586 844516 247234 > 2¹⁵¹ [i]