MinT - Best Known (160−70, 160, s)-Nets in Base 2

Best Known (160−70, 160, s)-Nets in Base 2

(160−70, 160, 54)-Net over F₂ — Constructive and digital

Digital (90, 160, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 80, 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]

(160−70, 160, 63)-Net over F₂ — Digital

Digital (90, 160, 63)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−70, 160, 282)-Net in Base 2 — Upper bound on s

There is no (90, 160, 283)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 605973 559608 594130 547319 923502 736351 010481 965744 > 2¹⁶⁰ [i]