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

Best Known (41, ∞, s)-Nets in Base 2

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

Digital (41, m, 33)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (41, 32)-sequence over F₂, using
- t-expansion [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, ∞, 49)-Net in Base 2 — Upper bound on s

There is no (41, m, 50)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (41, 292, 50)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²⁹², 50, S₂, 6, 251), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 206886 466346 471243 136639 015229 077469 481789 758731 696650 455233 014387 554350 757213 884221 751296 / 21 > 2²⁹² [i]