MinT - Best Known (41, 167, s)-Nets in Base 2

Best Known (41, 167, s)-Nets in Base 2

(41, 167, 33)-Net over F₂ — Constructive and digital

Digital (41, 167, 33)-net over F₂, using

t-expansion [i] based on digital (39, 167, 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]

(41, 167, 54)-Net in Base 2 — Upper bound on s

There is no (41, 167, 55)-net in base 2, because

9 times m-reduction [i] would yield (41, 158, 55)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁵⁸, 55, S₂, 3, 117), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 26 307029 471956 252527 666326 988893 094353 806785 773568 / 59 > 2¹⁵⁸ [i]