MinT - Best Known (73, 73+27, s)-Nets in Base 2

Best Known (73, 73+27, s)-Nets in Base 2

(73, 73+27, 84)-Net over F₂ — Constructive and digital

Digital (73, 100, 84)-net over F₂, using

2 times m-reduction [i] based on digital (73, 102, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 34, 28)-net over F₈, using
  - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
      - a function field by SÃ©mirat [i]

(73, 73+27, 134)-Net over F₂ — Digital

Digital (73, 100, 134)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+27, 1092)-Net in Base 2 — Upper bound on s

There is no (73, 100, 1093)-net in base 2, because

1 times m-reduction [i] would yield (73, 99, 1093)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 637300 831442 395235 915719 331472 > 2⁹⁹ [i]