MinT - Best Known (97−65, 97, s)-Nets in Base 8

Best Known (97−65, 97, s)-Nets in Base 8

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

Digital (32, 97, 65)-net over F₈, using

t-expansion [i] based on digital (14, 97, 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]

(97−65, 97, 97)-Net over F₈ — Digital

Digital (32, 97, 97)-net over F₈, using

t-expansion [i] based on digital (28, 97, 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]

(97−65, 97, 915)-Net in Base 8 — Upper bound on s

There is no (32, 97, 916)-net in base 8, because

1 times m-reduction [i] would yield (32, 96, 916)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 504 556355 659982 488140 979695 687864 057115 385766 501568 585274 114137 852895 106233 184431 901740 > 8⁹⁶ [i]