MinT - Best Known (159−125, 159, s)-Nets in Base 2

Best Known (159−125, 159, s)-Nets in Base 2

(159−125, 159, 24)-Net over F₂ — Constructive and digital

Digital (34, 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]

(159−125, 159, 28)-Net over F₂ — Digital

Digital (34, 159, 28)-net over F₂, using

t-expansion [i] based on digital (33, 159, 28)-net over F₂, using
- net from sequence [i] based on digital (33, 27)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 28, using
    - Drinfeld modules of rank 1 [i]

(159−125, 159, 46)-Net in Base 2 — Upper bound on s

There is no (34, 159, 47)-net in base 2, because

25 times m-reduction [i] would yield (34, 134, 47)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹³⁴, 47, S₂, 3, 100), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 3 136042 293543 368879 278460 382091 175836 778496 / 101 > 2¹³⁴ [i]