MinT - Best Known (85−51, 85, s)-Nets in Base 2

Best Known (85−51, 85, s)-Nets in Base 2

(85−51, 85, 24)-Net over F₂ — Constructive and digital

Digital (34, 85, 24)-net over F₂, using

t-expansion [i] based on digital (33, 85, 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]

(85−51, 85, 28)-Net over F₂ — Digital

Digital (34, 85, 28)-net over F₂, using

t-expansion [i] based on digital (33, 85, 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]

(85−51, 85, 72)-Net in Base 2 — Upper bound on s

There is no (34, 85, 73)-net in base 2, because

1 times m-reduction [i] would yield (34, 84, 73)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 21 720772 715717 738492 455304 > 2⁸⁴ [i]