MinT - Best Known (158, 158+47, s)-Nets in Base 2

Best Known (158, 158+47, s)-Nets in Base 2

(158, 158+47, 195)-Net over F₂ — Constructive and digital

Digital (158, 205, 195)-net over F₂, using

11 times m-reduction [i] based on digital (158, 216, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 72, 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]

(158, 158+47, 359)-Net over F₂ — Digital

Digital (158, 205, 359)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(158, 158+47, 4376)-Net in Base 2 — Upper bound on s

There is no (158, 205, 4377)-net in base 2, because

1 times m-reduction [i] would yield (158, 204, 4377)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 25 798119 662846 193803 348708 097644 842485 364869 555558 635118 137600 > 2²⁰⁴ [i]