MinT - Best Known (153, 153+104, s)-Nets in Base 2

Best Known (153, 153+104, s)-Nets in Base 2

(153, 153+104, 76)-Net over F₂ — Constructive and digital

Digital (153, 257, 76)-net over F₂, using

t-expansion [i] based on digital (152, 257, 76)-net over F₂, using
- 1 times m-reduction [i] based on digital (152, 258, 76)-net over F₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (45, 98, 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, 160, 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]

(153, 153+104, 111)-Net over F₂ — Digital

Digital (153, 257, 111)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(153, 153+104, 548)-Net in Base 2 — Upper bound on s

There is no (153, 257, 549)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 241872 246816 365374 675133 755975 090189 820900 297594 217098 279815 111578 260578 901152 > 2²⁵⁷ [i]