MinT - Best Known (157, 214, s)-Nets in Base 2

Best Known (157, 214, s)-Nets in Base 2

(157, 214, 195)-Net over F₂ — Constructive and digital

Digital (157, 214, 195)-net over F₂, using

2¹ times duplication [i] based on digital (156, 213, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 71, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(157, 214, 252)-Net over F₂ — Digital

Digital (157, 214, 252)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 214, 2161)-Net in Base 2 — Upper bound on s

There is no (157, 214, 2162)-net in base 2, because

1 times m-reduction [i] would yield (157, 213, 2162)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13215 119176 592154 252441 016541 167985 861255 489722 774222 511477 285880 > 2²¹³ [i]