MinT - Best Known (147, 147+101, s)-Nets in Base 2

Best Known (147, 147+101, s)-Nets in Base 2

(147, 147+101, 75)-Net over F₂ — Constructive and digital

Digital (147, 248, 75)-net over F₂, using

7 times m-reduction [i] based on digital (147, 255, 75)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (39, 93, 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, 162, 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]

(147, 147+101, 106)-Net over F₂ — Digital

Digital (147, 248, 106)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+101, 527)-Net in Base 2 — Upper bound on s

There is no (147, 248, 528)-net in base 2, because

1 times m-reduction [i] would yield (147, 247, 528)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 234 969475 403361 814431 395367 109538 691049 021155 740615 012270 823306 995190 152928 > 2²⁴⁷ [i]