MinT - Best Known (163, 163+50, s)-Nets in Base 2

Best Known (163, 163+50, s)-Nets in Base 2

(163, 163+50, 195)-Net over F₂ — Constructive and digital

Digital (163, 213, 195)-net over F₂, using

t-expansion [i] based on digital (162, 213, 195)-net over F₂, using
- 9 times m-reduction [i] based on digital (162, 222, 195)-net over F₂, using
  - trace code for nets [i] based on digital (14, 74, 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]

(163, 163+50, 348)-Net over F₂ — Digital

Digital (163, 213, 348)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+50, 3699)-Net in Base 2 — Upper bound on s

There is no (163, 213, 3700)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13241 826344 964996 944396 007668 660334 010290 028398 555886 413594 159524 > 2²¹³ [i]