MinT - Best Known (83−49, 83, s)-Nets in Base 2

Best Known (83−49, 83, s)-Nets in Base 2

(83−49, 83, 24)-Net over F₂ — Constructive and digital

Digital (34, 83, 24)-net over F₂, using

t-expansion [i] based on digital (33, 83, 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]

(83−49, 83, 28)-Net over F₂ — Digital

Digital (34, 83, 28)-net over F₂, using

t-expansion [i] based on digital (33, 83, 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]

(83−49, 83, 73)-Net in Base 2 — Upper bound on s

There is no (34, 83, 74)-net in base 2, because

1 times m-reduction [i] would yield (34, 82, 74)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 017991 548098 719295 996772 > 2⁸² [i]