MinT - Best Known (148, 148+110, s)-Nets in Base 2

Best Known (148, 148+110, s)-Nets in Base 2

(148, 148+110, 75)-Net over F₂ — Constructive and digital

Digital (148, 258, 75)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (39, 94, 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, 164, 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]

(148, 148+110, 99)-Net over F₂ — Digital

Digital (148, 258, 99)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+110, 474)-Net in Base 2 — Upper bound on s

There is no (148, 258, 475)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 496599 999152 847554 804688 160680 164591 877988 045543 079162 462335 326328 849272 555464 > 2²⁵⁸ [i]