MinT - Best Known (99−64, 99, s)-Nets in Base 8

Best Known (99−64, 99, s)-Nets in Base 8

(99−64, 99, 65)-Net over F₈ — Constructive and digital

Digital (35, 99, 65)-net over F₈, using

t-expansion [i] based on digital (14, 99, 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]

(99−64, 99, 112)-Net over F₈ — Digital

Digital (35, 99, 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]

(99−64, 99, 1116)-Net in Base 8 — Upper bound on s

There is no (35, 99, 1117)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 255184 532149 555610 631305 484058 503629 723262 718420 104573 067991 726580 233778 895924 122469 840394 > 8⁹⁹ [i]