MinT - Best Known (164−42, 164, s)-Nets in Base 2

Best Known (164−42, 164, s)-Nets in Base 2

(164−42, 164, 144)-Net over F₂ — Constructive and digital

Digital (122, 164, 144)-net over F₂, using

t-expansion [i] based on digital (121, 164, 144)-net over F₂, using
- 1 times m-reduction [i] based on digital (121, 165, 144)-net over F₂, using
  - trace code for nets [i] based on digital (11, 55, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]

(164−42, 164, 224)-Net over F₂ — Digital

Digital (122, 164, 224)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(164−42, 164, 1916)-Net in Base 2 — Upper bound on s

There is no (122, 164, 1917)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 23 549414 792199 565720 237632 650764 232108 481187 907926 > 2¹⁶⁴ [i]