MinT - Best Known (160−57, 160, s)-Nets in Base 2

Best Known (160−57, 160, s)-Nets in Base 2

(160−57, 160, 68)-Net over F₂ — Constructive and digital

Digital (103, 160, 68)-net over F₂, using

4 times m-reduction [i] based on digital (103, 164, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 82, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(160−57, 160, 100)-Net over F₂ — Digital

Digital (103, 160, 100)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−57, 160, 538)-Net in Base 2 — Upper bound on s

There is no (103, 160, 539)-net in base 2, because

1 times m-reduction [i] would yield (103, 159, 539)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 749746 177120 853237 482256 550478 339416 203922 437784 > 2¹⁵⁹ [i]