MinT - Best Known (115−40, 115, s)-Nets in Base 2

Best Known (115−40, 115, s)-Nets in Base 2

(115−40, 115, 66)-Net over F₂ — Constructive and digital

Digital (75, 115, 66)-net over F₂, using

5 times m-reduction [i] based on digital (75, 120, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 60, 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]

(115−40, 115, 81)-Net over F₂ — Digital

Digital (75, 115, 81)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−40, 115, 418)-Net in Base 2 — Upper bound on s

There is no (75, 115, 419)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 42911 243115 980389 485317 543902 449832 > 2¹¹⁵ [i]