MinT - Best Known (35, 35+112, s)-Nets in Base 8

Best Known (35, 35+112, s)-Nets in Base 8

(35, 35+112, 65)-Net over F₈ — Constructive and digital

Digital (35, 147, 65)-net over F₈, using

t-expansion [i] based on digital (14, 147, 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, 35+112, 112)-Net over F₈ — Digital

Digital (35, 147, 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, 35+112, 693)-Net in Base 8 — Upper bound on s

There is no (35, 147, 694)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 108146 751021 269030 696151 868440 422566 268848 432382 500703 620776 720449 458474 233885 638207 402109 074886 425957 849446 133074 122907 890203 610032 > 8¹⁴⁷ [i]