MinT - Best Known (131−50, 131, s)-Nets in Base 2

Best Known (131−50, 131, s)-Nets in Base 2

(131−50, 131, 66)-Net over F₂ — Constructive and digital

Digital (81, 131, 66)-net over F₂, using

1 times m-reduction [i] based on digital (81, 132, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 66, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(131−50, 131, 73)-Net over F₂ — Digital

Digital (81, 131, 73)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−50, 131, 349)-Net in Base 2 — Upper bound on s

There is no (81, 131, 350)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2876 487617 109030 628476 080699 516135 141265 > 2¹³¹ [i]