MinT - Best Known (44, 44+34, s)-Nets in Base 2

Best Known (44, 44+34, s)-Nets in Base 2

(44, 44+34, 34)-Net over F₂ — Constructive and digital

Digital (44, 78, 34)-net over F₂, using

trace code for nets [i] based on digital (5, 39, 17)-net over F₄, using
- net from sequence [i] based on digital (5, 16)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]

(44, 44+34, 37)-Net over F₂ — Digital

Digital (44, 78, 37)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 44+34, 144)-Net in Base 2 — Upper bound on s

There is no (44, 78, 145)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2⁷⁸, 145, S₂, 34), but
- the linear programming bound shows that MÂ â‰¥ 6 452658 897421 925882 991923 762933 214377 859980 440698 591468 415644 336128 / 20 712793 240469 221474 764436 259197 787149 263939 > 2⁷⁸ [i]