MinT - Best Known (134, 134+82, s)-Nets in Base 2

Best Known (134, 134+82, s)-Nets in Base 2

(134, 134+82, 75)-Net over F₂ — Constructive and digital

Digital (134, 216, 75)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 80, 33)-net over F₂, using
  - net from sequence [i] based on digital (39, 32)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
2. digital (54, 136, 42)-net over F₂, using
  - net from sequence [i] based on digital (54, 41)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
      - an explicitly constructive algebraic function field [i]

(134, 134+82, 111)-Net over F₂ — Digital

Digital (134, 216, 111)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 134+82, 563)-Net in Base 2 — Upper bound on s

There is no (134, 216, 564)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 107771 908920 831897 464615 456961 811744 417983 278755 429795 247315 970450 > 2²¹⁶ [i]