MinT - Best Known (101−78, 101, s)-Nets in Base 8

Best Known (101−78, 101, s)-Nets in Base 8

(101−78, 101, 65)-Net over F₈ — Constructive and digital

Digital (23, 101, 65)-net over F₈, using

t-expansion [i] based on digital (14, 101, 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]

(101−78, 101, 76)-Net over F₈ — Digital

Digital (23, 101, 76)-net over F₈, using

t-expansion [i] based on digital (20, 101, 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]

(101−78, 101, 455)-Net in Base 8 — Upper bound on s

There is no (23, 101, 456)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 16 770495 066689 803703 161890 018983 959329 137180 505381 894548 639608 549482 592429 655839 475002 736694 > 8¹⁰¹ [i]