MinT - Best Known (23, 23+29, s)-Nets in Base 8

Best Known (23, 23+29, s)-Nets in Base 8

(23, 23+29, 65)-Net over F₈ — Constructive and digital

Digital (23, 52, 65)-net over F₈, using

t-expansion [i] based on digital (14, 52, 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+29, 76)-Net over F₈ — Digital

Digital (23, 52, 76)-net over F₈, using

t-expansion [i] based on digital (20, 52, 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+29, 81)-Net in Base 8

(23, 52, 81)-net in base 8, using

base change [i] based on digital (10, 39, 81)-net over F₁₆, using
- net from sequence [i] based on digital (10, 80)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 10 and N(F) ≥ 81, using
    - a curve from the manYPoints database [i]

(23, 23+29, 1674)-Net in Base 8 — Upper bound on s

There is no (23, 52, 1675)-net in base 8, because

1 times m-reduction [i] would yield (23, 51, 1675)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11426 117643 799421 748368 595957 192514 387726 263136 > 8⁵¹ [i]