MinT - Best Known (244−99, 244, s)-Nets in Base 2

Best Known (244−99, 244, s)-Nets in Base 2

(244−99, 244, 75)-Net over F₂ — Constructive and digital

Digital (145, 244, 75)-net over F₂, using

5 times m-reduction [i] based on digital (145, 249, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 91, 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, 158, 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]

(244−99, 244, 106)-Net over F₂ — Digital

Digital (145, 244, 106)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−99, 244, 525)-Net in Base 2 — Upper bound on s

There is no (145, 244, 526)-net in base 2, because

1 times m-reduction [i] would yield (145, 243, 526)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14 889076 332241 778337 803043 176347 726881 928629 325594 698990 969454 817929 505568 > 2²⁴³ [i]