MinT - Best Known (23, 23+89, s)-Nets in Base 8

Best Known (23, 23+89, s)-Nets in Base 8

(23, 23+89, 65)-Net over F₈ — Constructive and digital

Digital (23, 112, 65)-net over F₈, using

t-expansion [i] based on digital (14, 112, 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]

(23, 23+89, 76)-Net over F₈ — Digital

Digital (23, 112, 76)-net over F₈, using

t-expansion [i] based on digital (20, 112, 76)-net over F₈, using
- net from sequence [i] based on digital (20, 75)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 20 and N(F) ≥ 76, using
    - a curve from the manYPoints database [i]

(23, 23+89, 440)-Net in Base 8 — Upper bound on s

There is no (23, 112, 441)-net in base 8, because

1 times m-reduction [i] would yield (23, 111, 441)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 18306 489769 836280 798093 941608 273818 527667 651545 983102 076515 205756 460553 085481 360515 299059 016390 623380 > 8¹¹¹ [i]