MinT - Best Known (73, 73+29, s)-Nets in Base 2

Best Known (73, 73+29, s)-Nets in Base 2

(73, 73+29, 84)-Net over F₂ — Constructive and digital

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+29, 120)-Net over F₂ — Digital

Digital (73, 102, 120)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+29, 877)-Net in Base 2 — Upper bound on s

There is no (73, 102, 878)-net in base 2, because

1 times m-reduction [i] would yield (73, 101, 878)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 555231 899764 876907 455791 262696 > 2¹⁰¹ [i]