MinT - Best Known (100−69, 100, s)-Nets in Base 8

Best Known (100−69, 100, s)-Nets in Base 8

(100−69, 100, 65)-Net over F₈ — Constructive and digital

Digital (31, 100, 65)-net over F₈, using

t-expansion [i] based on digital (14, 100, 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]

(100−69, 100, 97)-Net over F₈ — Digital

Digital (31, 100, 97)-net over F₈, using

t-expansion [i] based on digital (28, 100, 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]

(100−69, 100, 802)-Net in Base 8 — Upper bound on s

There is no (31, 100, 803)-net in base 8, because

1 times m-reduction [i] would yield (31, 99, 803)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 255910 520366 769231 721742 453977 239546 882604 481874 252260 056540 335157 400916 732817 719171 496089 > 8⁹⁹ [i]