MinT - Best Known (38, ∞, s)-Nets in Base 2

Best Known (38, ∞, s)-Nets in Base 2

(38, ∞, 24)-Net over F₂ — Constructive and digital

Digital (38, m, 24)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (38, 23)-sequence over F₂, using
- t-expansion [i] based on digital (33, 23)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]

(38, ∞, 30)-Net over F₂ — Digital

Digital (38, m, 30)-net over F₂ for arbitrarily large m, using

net from sequence [i] based on digital (38, 29)-sequence over F₂, using
- t-expansion [i] based on digital (36, 29)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 36 and N(F) ≥ 30, using
    - Drinfeld modules of rank 1 [i]

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

There is no (38, m, 47)-net in base 2 for arbitrarily large m, because

m-reduction [i] would yield (38, 228, 47)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²²⁸, 47, S₂, 5, 190), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 84546 392748 184406 396075 759312 893561 792526 084909 087235 300740 921741 541376 / 191 > 2²²⁸ [i]