MinT - Best Known (137−112, 137, s)-Nets in Base 8

Best Known (137−112, 137, s)-Nets in Base 8

(137−112, 137, 65)-Net over F₈ — Constructive and digital

Digital (25, 137, 65)-net over F₈, using

t-expansion [i] based on digital (14, 137, 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]

(137−112, 137, 86)-Net over F₈ — Digital

Digital (25, 137, 86)-net over F₈, using

net from sequence [i] based on digital (25, 85)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
  - a curve from the manYPoints database [i]

(137−112, 137, 467)-Net in Base 8 — Upper bound on s

There is no (25, 137, 468)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5622 195860 346313 572720 183229 831954 934404 966126 149976 768634 055522 010348 839738 117637 797022 275677 065461 694849 312854 429031 574296 > 8¹³⁷ [i]