MinT - Best Known (173−39, 173, s)-Nets in Base 2

Best Known (173−39, 173, s)-Nets in Base 2

(173−39, 173, 195)-Net over F₂ — Constructive and digital

Digital (134, 173, 195)-net over F₂, using

7 times m-reduction [i] based on digital (134, 180, 195)-net over F₂, using
- trace code for nets [i] based on digital (14, 60, 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]

(173−39, 173, 326)-Net over F₂ — Digital

Digital (134, 173, 326)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−39, 173, 4182)-Net in Base 2 — Upper bound on s

There is no (134, 173, 4183)-net in base 2, because

1 times m-reduction [i] would yield (134, 172, 4183)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5998 732195 464211 553276 160291 164582 127863 236817 679470 > 2¹⁷² [i]