MinT - Best Known (23, 23+102, s)-Nets in Base 8

Best Known (23, 23+102, s)-Nets in Base 8

(23, 23+102, 65)-Net over F₈ — Constructive and digital

Digital (23, 125, 65)-net over F₈, using

t-expansion [i] based on digital (14, 125, 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+102, 76)-Net over F₈ — Digital

Digital (23, 125, 76)-net over F₈, using

t-expansion [i] based on digital (20, 125, 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+102, 432)-Net in Base 8 — Upper bound on s

There is no (23, 125, 433)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 85412 050653 721404 192584 042971 389888 691390 529667 966884 020398 887437 202508 190142 103600 183034 084542 445137 786524 498304 > 8¹²⁵ [i]