MinT - Best Known (235−93, 235, s)-Nets in Base 2

Best Known (235−93, 235, s)-Nets in Base 2

(235−93, 235, 75)-Net over F₂ — Constructive and digital

Digital (142, 235, 75)-net over F₂, using

5 times m-reduction [i] based on digital (142, 240, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 88, 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, 152, 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]

(235−93, 235, 108)-Net over F₂ — Digital

Digital (142, 235, 108)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−93, 235, 546)-Net in Base 2 — Upper bound on s

There is no (142, 235, 547)-net in base 2, because

1 times m-reduction [i] would yield (142, 234, 547)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28595 546359 650311 041323 249659 943343 114568 584117 560844 312659 779513 746304 > 2²³⁴ [i]