MinT - Best Known (35, 167, s)-Nets in Base 8

Best Known (35, 167, s)-Nets in Base 8

(35, 167, 65)-Net over F₈ — Constructive and digital

Digital (35, 167, 65)-net over F₈, using

t-expansion [i] based on digital (14, 167, 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]

(35, 167, 112)-Net over F₈ — Digital

Digital (35, 167, 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]

(35, 167, 658)-Net in Base 8 — Upper bound on s

There is no (35, 167, 659)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 679717 395399 854569 484864 950906 581236 757671 933246 874311 029191 303243 500239 008809 020236 505786 190788 255832 387572 567088 126838 136269 287613 697870 652060 114934 > 8¹⁶⁷ [i]