MinT - Best Known (233−93, 233, s)-Nets in Base 2

Best Known (233−93, 233, s)-Nets in Base 2

(233−93, 233, 75)-Net over F₂ — Constructive and digital

Digital (140, 233, 75)-net over F₂, using

1 times m-reduction [i] based on digital (140, 234, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 86, 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, 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]

(233−93, 233, 106)-Net over F₂ — Digital

Digital (140, 233, 106)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−93, 233, 528)-Net in Base 2 — Upper bound on s

There is no (140, 233, 529)-net in base 2, because

1 times m-reduction [i] would yield (140, 232, 529)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7193 177932 629101 568378 171638 524597 259869 194970 525535 537877 831333 974400 > 2²³² [i]