MinT - Best Known (156, 156+104, s)-Nets in Base 2

Best Known (156, 156+104, s)-Nets in Base 2

(156, 156+104, 77)-Net over F₂ — Constructive and digital

Digital (156, 260, 77)-net over F₂, using

2¹ times duplication [i] based on digital (155, 259, 77)-net over F₂, using
- t-expansion [i] based on digital (154, 259, 77)-net over F₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (48, 100, 35)-net over F₂, using
      - net from sequence [i] based on digital (48, 34)-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 2 places 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, 159, 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]

(156, 156+104, 116)-Net over F₂ — Digital

Digital (156, 260, 116)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 156+104, 573)-Net in Base 2 — Upper bound on s

There is no (156, 260, 574)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 897813 963366 361093 988423 642528 305448 418552 246269 423742 345718 196245 495581 184977 > 2²⁶⁰ [i]