MinT - Best Known (219−184, 219, s)-Nets in Base 2

Best Known (219−184, 219, s)-Nets in Base 2

(219−184, 219, 24)-Net over F₂ — Constructive and digital

Digital (35, 219, 24)-net over F₂, using

t-expansion [i] based on digital (33, 219, 24)-net over F₂, using
- net from sequence [i] based on digital (33, 23)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]

(219−184, 219, 29)-Net over F₂ — Digital

Digital (35, 219, 29)-net over F₂, using

net from sequence [i] based on digital (35, 28)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 35 and N(F) ≥ 29, using
  - a curve from the manYPoints database [i]

(219−184, 219, 43)-Net in Base 2 — Upper bound on s

There is no (35, 219, 44)-net in base 2, because

6 times m-reduction [i] would yield (35, 213, 44)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²¹³, 44, S₂, 5, 178), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 2 738119 583382 486854 145868 719775 431240 291272 480414 276892 612085 415936 / 179 > 2²¹³ [i]