MinT - Best Known (50−38, 50, s)-Nets in Base 2

Best Known (50−38, 50, s)-Nets in Base 2

(50−38, 50, 14)-Net over F₂ — Constructive and digital

Digital (12, 50, 14)-net over F₂, using

t-expansion [i] based on digital (11, 50, 14)-net over F₂, using
- net from sequence [i] based on digital (11, 13)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 11 and N(F) ≥ 14, using
    - an explicitly constructive algebraic function field [i]

(50−38, 50, 22)-Net in Base 2 — Upper bound on s

There is no (12, 50, 23)-net in base 2, because

13 times m-reduction [i] would yield (12, 37, 23)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2³⁷, 23, S₂, 2, 25), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 701 058921 791488 / 4361 > 2³⁷ [i]