MinT - Best Known (203−168, 203, s)-Nets in Base 2

Best Known (203−168, 203, s)-Nets in Base 2

(203−168, 203, 24)-Net over F₂ — Constructive and digital

Digital (35, 203, 24)-net over F₂, using

t-expansion [i] based on digital (33, 203, 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]

(203−168, 203, 29)-Net over F₂ — Digital

Digital (35, 203, 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]

(203−168, 203, 44)-Net in Base 2 — Upper bound on s

There is no (35, 203, 45)-net in base 2, because

30 times m-reduction [i] would yield (35, 173, 45)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁷³, 45, S₂, 4, 138), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1 819838 454778 243019 300537 094740 992155 547252 707593 027584 / 139 > 2¹⁷³ [i]