MinT - Best Known (240−94, 240, s)-Nets in Base 2

Best Known (240−94, 240, s)-Nets in Base 2

(240−94, 240, 76)-Net over F₂ — Constructive and digital

Digital (146, 240, 76)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (45, 92, 34)-net over F₂, using
  - net from sequence [i] based on digital (45, 33)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 41, N(F)Â =Â 32, 1 place with degree 2, and 1 place with degree 4 [i] based on function field F/F₂ with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
2. digital (54, 148, 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]

(240−94, 240, 113)-Net over F₂ — Digital

Digital (146, 240, 113)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(240−94, 240, 566)-Net in Base 2 — Upper bound on s

There is no (146, 240, 567)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 881938 300204 433945 113722 196262 964496 105720 965416 631144 123750 650747 512404 > 2²⁴⁰ [i]