MinT - Best Known (245−98, 245, s)-Nets in Base 2

Best Known (245−98, 245, s)-Nets in Base 2

(245−98, 245, 76)-Net over F₂ — Constructive and digital

Digital (147, 245, 76)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 88, 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 (59, 157, 43)-net over F₂, using
  - net from sequence [i] based on digital (59, 42)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 54, N(F)Â =Â 42, and 1 place with degree 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]

(245−98, 245, 110)-Net over F₂ — Digital

Digital (147, 245, 110)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−98, 245, 542)-Net in Base 2 — Upper bound on s

There is no (147, 245, 543)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 59 661636 658692 494746 555434 230982 607310 888385 023443 501084 727247 940138 805504 > 2²⁴⁵ [i]