MinT - Best Known (168−132, 168, s)-Nets in Base 8

Best Known (168−132, 168, s)-Nets in Base 8

(168−132, 168, 65)-Net over F₈ — Constructive and digital

Digital (36, 168, 65)-net over F₈, using

t-expansion [i] based on digital (14, 168, 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]

(168−132, 168, 112)-Net over F₈ — Digital

Digital (36, 168, 112)-net over F₈, using

t-expansion [i] based on digital (35, 168, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(168−132, 168, 681)-Net in Base 8 — Upper bound on s

There is no (36, 168, 682)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 56 504552 191282 575993 916528 606586 369169 961677 366366 624868 077554 399340 818150 526344 856459 990411 871621 360941 108182 761900 218140 608772 037123 769878 248615 846440 > 8¹⁶⁸ [i]