MinT - Best Known (40, 72, s)-Nets in Base 2

Best Known (40, 72, s)-Nets in Base 2

(40, 72, 33)-Net over F₂ — Constructive and digital

Digital (40, 72, 33)-net over F₂, using

t-expansion [i] based on digital (39, 72, 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]

(40, 72, 125)-Net in Base 2 — Upper bound on s

There is no (40, 72, 126)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2⁷², 126, S₂, 32), but
- the linear programming bound shows that MÂ â‰¥ 163 005211 721460 055257 870637 096174 404209 999872 / 34370 163308 084940 061297 > 2⁷² [i]