MinT - Best Known (87−51, 87, s)-Nets in Base 8

Best Known (87−51, 87, s)-Nets in Base 8

(87−51, 87, 65)-Net over F₈ — Constructive and digital

Digital (36, 87, 65)-net over F₈, using

t-expansion [i] based on digital (14, 87, 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]

(87−51, 87, 112)-Net over F₈ — Digital

Digital (36, 87, 112)-net over F₈, using

t-expansion [i] based on digital (35, 87, 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]

(87−51, 87, 1842)-Net in Base 8 — Upper bound on s

There is no (36, 87, 1843)-net in base 8, because

1 times m-reduction [i] would yield (36, 86, 1843)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 463502 270268 654411 140997 523206 613213 109498 780941 925926 125187 492411 436100 750824 > 8⁸⁶ [i]