MinT - Best Known (131−34, 131, s)-Nets in Base 2

Best Known (131−34, 131, s)-Nets in Base 2

(131−34, 131, 135)-Net over F₂ — Constructive and digital

Digital (97, 131, 135)-net over F₂, using

1 times m-reduction [i] based on digital (97, 132, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 44, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(131−34, 131, 181)-Net over F₂ — Digital

Digital (97, 131, 181)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−34, 131, 1473)-Net in Base 2 — Upper bound on s

There is no (97, 131, 1474)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2732 969161 717220 347203 205509 785185 915404 > 2¹³¹ [i]