MinT - Best Known (168−138, 168, s)-Nets in Base 8

Best Known (168−138, 168, s)-Nets in Base 8

(168−138, 168, 65)-Net over F₈ — Constructive and digital

Digital (30, 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]

(168−138, 168, 97)-Net over F₈ — Digital

Digital (30, 168, 97)-net over F₈, using

t-expansion [i] based on digital (28, 168, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(168−138, 168, 556)-Net in Base 8 — Upper bound on s

There is no (30, 168, 557)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 58 443534 962900 252429 582772 454358 443961 810592 590961 245838 282600 019169 821896 560680 091818 711887 687013 566635 048171 289835 396715 154501 659272 086416 634538 516224 > 8¹⁶⁸ [i]