MinT - Best Known (44, ∞, s)-Nets in Base 2

Best Known (44, ∞, s)-Nets in Base 2

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

Digital (44, m, 33)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (44, 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]

(44, ∞, 34)-Net over F₂ — Digital

Digital (44, m, 34)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (44, 33)-sequence over F₂, using
- t-expansion [i] based on digital (43, 33)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 43 and N(F) ≥ 34, using
    - a curve from the manYPoints database [i]

(44, ∞, 52)-Net in Base 2 — Upper bound on s

There is no (44, m, 53)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (44, 310, 53)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2³¹⁰, 53, S₂, 6, 266), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 208592 483976 651375 233888 838493 120323 691670 363511 391872 065140 782013 888645 095765 678713 179891 302400 / 89 > 2³¹⁰ [i]