MinT - Best Known (99−69, 99, s)-Nets in Base 8

Best Known (99−69, 99, s)-Nets in Base 8

(99−69, 99, 65)-Net over F₈ — Constructive and digital

Digital (30, 99, 65)-net over F₈, using

t-expansion [i] based on digital (14, 99, 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]

(99−69, 99, 97)-Net over F₈ — Digital

Digital (30, 99, 97)-net over F₈, using

t-expansion [i] based on digital (28, 99, 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]

(99−69, 99, 753)-Net in Base 8 — Upper bound on s

There is no (30, 99, 754)-net in base 8, because

1 times m-reduction [i] would yield (30, 98, 754)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 31829 929744 260141 914882 681120 914489 248069 977548 863052 433132 028027 124077 064712 858916 859192 > 8⁹⁸ [i]