MinT - Best Known (89−53, 89, s)-Nets in Base 8

Best Known (89−53, 89, s)-Nets in Base 8

(89−53, 89, 65)-Net over F₈ — Constructive and digital

Digital (36, 89, 65)-net over F₈, using

t-expansion [i] based on digital (14, 89, 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]

(89−53, 89, 112)-Net over F₈ — Digital

Digital (36, 89, 112)-net over F₈, using

t-expansion [i] based on digital (35, 89, 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]

(89−53, 89, 1700)-Net in Base 8 — Upper bound on s

There is no (36, 89, 1701)-net in base 8, because

1 times m-reduction [i] would yield (36, 88, 1701)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 29 652215 055758 291514 908040 822624 854826 075034 032940 275753 174198 997181 539626 916552 > 8⁸⁸ [i]