MinT - Best Known (95−59, 95, s)-Nets in Base 8

Best Known (95−59, 95, s)-Nets in Base 8

(95−59, 95, 65)-Net over F₈ — Constructive and digital

Digital (36, 95, 65)-net over F₈, using

t-expansion [i] based on digital (14, 95, 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]

(95−59, 95, 112)-Net over F₈ — Digital

Digital (36, 95, 112)-net over F₈, using

t-expansion [i] based on digital (35, 95, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(95−59, 95, 1392)-Net in Base 8 — Upper bound on s

There is no (36, 95, 1393)-net in base 8, because

1 times m-reduction [i] would yield (36, 94, 1393)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 7 910893 931076 698013 207192 140018 616768 438063 497612 194347 547076 359639 715757 107068 983392 > 8⁹⁴ [i]