MinT - Best Known (35, 35+124, s)-Nets in Base 2

Best Known (35, 35+124, s)-Nets in Base 2

(35, 35+124, 24)-Net over F₂ — Constructive and digital

Digital (35, 159, 24)-net over F₂, using

t-expansion [i] based on digital (33, 159, 24)-net over F₂, using
- net from sequence [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]

(35, 35+124, 29)-Net over F₂ — Digital

Digital (35, 159, 29)-net over F₂, using

net from sequence [i] based on digital (35, 28)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 35 and N(F) ≥ 29, using
  - a curve from the manYPoints database [i]

(35, 35+124, 47)-Net in Base 2 — Upper bound on s

There is no (35, 159, 48)-net in base 2, because

22 times m-reduction [i] would yield (35, 137, 48)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹³⁷, 48, S₂, 3, 102), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 22 300745 198530 623141 535718 272648 361505 980416 / 103 > 2¹³⁷ [i]