MinT - Best Known (171, 171+89, s)-Nets in Base 2

Best Known (171, 171+89, s)-Nets in Base 2

(171, 171+89, 112)-Net over F₂ — Constructive and digital

Digital (171, 260, 112)-net over F₂, using

t-expansion [i] based on digital (163, 260, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 130, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(171, 171+89, 164)-Net over F₂ — Digital

Digital (171, 260, 164)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+89, 957)-Net in Base 2 — Upper bound on s

There is no (171, 260, 958)-net in base 2, because

1 times m-reduction [i] would yield (171, 259, 958)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 964982 526871 297088 156403 278281 140820 171585 754784 445086 480617 895410 747080 094205 > 2²⁵⁹ [i]