MinT - Best Known (160−61, 160, s)-Nets in Base 2

Best Known (160−61, 160, s)-Nets in Base 2

(160−61, 160, 66)-Net over F₂ — Constructive and digital

Digital (99, 160, 66)-net over F₂, using

8 times m-reduction [i] based on digital (99, 168, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 84, 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]

(160−61, 160, 86)-Net over F₂ — Digital

Digital (99, 160, 86)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−61, 160, 431)-Net in Base 2 — Upper bound on s

There is no (99, 160, 432)-net in base 2, because

1 times m-reduction [i] would yield (99, 159, 432)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 738867 218401 862590 959932 558553 908693 533727 618462 > 2¹⁵⁹ [i]