MinT - Best Known (82−38, 82, s)-Nets in Base 2

Best Known (82−38, 82, s)-Nets in Base 2

(82−38, 82, 33)-Net over F₂ — Constructive and digital

Digital (44, 82, 33)-net over F₂, using

t-expansion [i] based on digital (39, 82, 33)-net over F₂, using
- net from sequence [i] based on digital (39, 32)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(82−38, 82, 34)-Net over F₂ — Digital

Digital (44, 82, 34)-net over F₂, using

t-expansion [i] based on digital (43, 82, 34)-net over F₂, using
- net from sequence [i] based on digital (43, 33)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 43 and N(F) ≥ 34, using
    - a curve from the manYPoints database [i]

(82−38, 82, 115)-Net in Base 2 — Upper bound on s

There is no (44, 82, 116)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2⁸², 116, S₂, 38), but
- the linear programming bound shows that MÂ â‰¥ 1 062617 333342 845814 746138 360785 403904 / 188306 971237 > 2⁸² [i]