MinT - Best Known (84−61, 84, s)-Nets in Base 8

Best Known (84−61, 84, s)-Nets in Base 8

(84−61, 84, 65)-Net over F₈ — Constructive and digital

Digital (23, 84, 65)-net over F₈, using

t-expansion [i] based on digital (14, 84, 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]

(84−61, 84, 76)-Net over F₈ — Digital

Digital (23, 84, 76)-net over F₈, using

t-expansion [i] based on digital (20, 84, 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]

(84−61, 84, 523)-Net in Base 8 — Upper bound on s

There is no (23, 84, 524)-net in base 8, because

1 times m-reduction [i] would yield (23, 83, 524)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 919 180838 647533 081243 586172 294519 860345 596239 880412 975023 743201 722360 633728 > 8⁸³ [i]