MinT - Best Known (131−55, 131, s)-Nets in Base 2

Best Known (131−55, 131, s)-Nets in Base 2

(131−55, 131, 54)-Net over F₂ — Constructive and digital

Digital (76, 131, 54)-net over F₂, using

1 times m-reduction [i] based on digital (76, 132, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 66, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(131−55, 131, 59)-Net over F₂ — Digital

Digital (76, 131, 59)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−55, 131, 269)-Net in Base 2 — Upper bound on s

There is no (76, 131, 270)-net in base 2, because

1 times m-reduction [i] would yield (76, 130, 270)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1398 622172 471817 503815 942965 508696 774112 > 2¹³⁰ [i]