MinT - Best Known (111−89, 111, s)-Nets in Base 8

Best Known (111−89, 111, s)-Nets in Base 8

(111−89, 111, 65)-Net over F₈ — Constructive and digital

Digital (22, 111, 65)-net over F₈, using

t-expansion [i] based on digital (14, 111, 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]

(111−89, 111, 76)-Net over F₈ — Digital

Digital (22, 111, 76)-net over F₈, using

t-expansion [i] based on digital (20, 111, 76)-net over F₈, using
- net from sequence [i] based on digital (20, 75)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 20 and N(F) ≥ 76, using
    - a curve from the manYPoints database [i]

(111−89, 111, 418)-Net in Base 8 — Upper bound on s

There is no (22, 111, 419)-net in base 8, because

1 times m-reduction [i] would yield (22, 110, 419)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2198 399912 813702 140773 455003 010249 684096 951464 272646 655323 395896 754478 038522 758106 331178 265340 547360 > 8¹¹⁰ [i]