MinT - Best Known (181, 181+63, s)-Nets in Base 2

Best Known (181, 181+63, s)-Nets in Base 2

(181, 181+63, 195)-Net over F₂ — Constructive and digital

Digital (181, 244, 195)-net over F₂, using

t-expansion [i] based on digital (180, 244, 195)-net over F₂, using
- 5 times m-reduction [i] based on digital (180, 249, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 83, 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]

(181, 181+63, 304)-Net over F₂ — Digital

Digital (181, 244, 304)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(181, 181+63, 2796)-Net in Base 2 — Upper bound on s

There is no (181, 244, 2797)-net in base 2, because

1 times m-reduction [i] would yield (181, 243, 2797)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14 140358 927889 885698 664431 819261 544780 295595 787503 138151 650957 551874 794704 > 2²⁴³ [i]