MinT - Best Known (101−72, 101, s)-Nets in Base 8

Best Known (101−72, 101, s)-Nets in Base 8

(101−72, 101, 65)-Net over F₈ — Constructive and digital

Digital (29, 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]

(101−72, 101, 97)-Net over F₈ — Digital

Digital (29, 101, 97)-net over F₈, using

t-expansion [i] based on digital (28, 101, 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]

(101−72, 101, 674)-Net in Base 8 — Upper bound on s

There is no (29, 101, 675)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 16 550650 323241 646008 697856 009920 009055 642581 219138 500016 008067 801188 023083 322480 926034 878240 > 8¹⁰¹ [i]