MinT - Best Known (204−57, 204, s)-Nets in Base 2

Best Known (204−57, 204, s)-Nets in Base 2

(204−57, 204, 144)-Net over F₂ — Constructive and digital

Digital (147, 204, 144)-net over F₂, using

trace code for nets [i] based on digital (11, 68, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(204−57, 204, 215)-Net over F₂ — Digital

Digital (147, 204, 215)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−57, 204, 1678)-Net in Base 2 — Upper bound on s

There is no (147, 204, 1679)-net in base 2, because

1 times m-reduction [i] would yield (147, 203, 1679)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12 912044 734877 193705 568852 388163 415243 713103 937352 618559 202712 > 2²⁰³ [i]