MinT - Best Known (119−97, 119, s)-Nets in Base 8

Best Known (119−97, 119, s)-Nets in Base 8

(119−97, 119, 65)-Net over F₈ — Constructive and digital

Digital (22, 119, 65)-net over F₈, using

t-expansion [i] based on digital (14, 119, 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]

(119−97, 119, 76)-Net over F₈ — Digital

Digital (22, 119, 76)-net over F₈, using

t-expansion [i] based on digital (20, 119, 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]

(119−97, 119, 414)-Net in Base 8 — Upper bound on s

There is no (22, 119, 415)-net in base 8, because

1 times m-reduction [i] would yield (22, 118, 415)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 38028 554301 483002 476350 720344 812697 161791 162989 622434 983008 956811 786494 909557 226463 705783 501957 110416 486580 > 8¹¹⁸ [i]