MinT - Best Known (86−51, 86, s)-Nets in Base 8

Best Known (86−51, 86, s)-Nets in Base 8

(86−51, 86, 65)-Net over F₈ — Constructive and digital

Digital (35, 86, 65)-net over F₈, using

t-expansion [i] based on digital (14, 86, 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]

(86−51, 86, 112)-Net over F₈ — Digital

Digital (35, 86, 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]

(86−51, 86, 1694)-Net in Base 8 — Upper bound on s

There is no (35, 86, 1695)-net in base 8, because

1 times m-reduction [i] would yield (35, 85, 1695)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 58218 160228 117640 849530 123348 424495 739179 171495 509220 149448 616964 824067 980622 > 8⁸⁵ [i]