MinT - Best Known (30, ∞, s)-Nets in Base 2

Best Known (30, ∞, s)-Nets in Base 2

(30, ∞, 21)-Net over F₂ — Constructive and digital

Digital (30, m, 21)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (30, 20)-sequence over F₂, using
- t-expansion [i] based on digital (21, 20)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(30, ∞, 25)-Net over F₂ — Digital

Digital (30, m, 25)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (30, 24)-sequence over F₂, using
- t-expansion [i] based on digital (28, 24)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 28 and N(F) ≥ 25, using
    - a curve from the manYPoints database [i]

(30, ∞, 38)-Net in Base 2 — Upper bound on s

There is no (30, m, 39)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (30, 187, 39)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁸⁷, 39, S₂, 5, 157), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 19615 942923 083377 386986 841947 523957 550319 860763 950107 852800 / 79 > 2¹⁸⁷ [i]