MinT - Best Known (113−83, 113, s)-Nets in Base 8

Best Known (113−83, 113, s)-Nets in Base 8

(113−83, 113, 65)-Net over F₈ — Constructive and digital

Digital (30, 113, 65)-net over F₈, using

t-expansion [i] based on digital (14, 113, 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]

(113−83, 113, 97)-Net over F₈ — Digital

Digital (30, 113, 97)-net over F₈, using

t-expansion [i] based on digital (28, 113, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(113−83, 113, 650)-Net in Base 8 — Upper bound on s

There is no (30, 113, 651)-net in base 8, because

1 times m-reduction [i] would yield (30, 112, 651)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 146947 971911 695945 812624 118361 842306 934557 769304 732213 433043 129055 002588 548546 043451 885339 095902 435400 > 8¹¹² [i]