MinT - Best Known (131−29, 131, s)-Nets in Base 2

Best Known (131−29, 131, s)-Nets in Base 2

(131−29, 131, 195)-Net over F₂ — Constructive and digital

Digital (102, 131, 195)-net over F₂, using

1 times m-reduction [i] based on digital (102, 132, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 44, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(131−29, 131, 276)-Net over F₂ — Digital

Digital (102, 131, 276)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−29, 131, 3752)-Net in Base 2 — Upper bound on s

There is no (102, 131, 3753)-net in base 2, because

1 times m-reduction [i] would yield (102, 130, 3753)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1361 230496 243771 667263 939252 773290 036496 > 2¹³⁰ [i]