MinT - Best Known (10, 10+167, s)-Nets in Base 2

Best Known (10, 10+167, s)-Nets in Base 2

(10, 10+167, 12)-Net over F₂ — Constructive and digital

Digital (10, 177, 12)-net over F₂, using

t-expansion [i] based on digital (9, 177, 12)-net over F₂, using
- net from sequence [i] based on digital (9, 11)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 9 and N(F) ≥ 12, using
    - an explicitly constructive algebraic function field [i]

(10, 10+167, 13)-Net over F₂ — Digital

Digital (10, 177, 13)-net over F₂, using

net from sequence [i] based on digital (10, 12)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 10 and N(F) ≥ 13, using
  - a curve from the manYPoints database [i]

(10, 10+167, 16)-Net in Base 2 — Upper bound on s

There is no (10, 177, 17)-net in base 2, because

115 times m-reduction [i] would yield (10, 62, 17)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2⁶², 17, S₂, 4, 52), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 276 701161 105643 274240 / 53 > 2⁶² [i]