MinT - Best Known (28, 28+81, s)-Nets in Base 8

Best Known (28, 28+81, s)-Nets in Base 8

(28, 28+81, 65)-Net over F₈ — Constructive and digital

Digital (28, 109, 65)-net over F₈, using

t-expansion [i] based on digital (14, 109, 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]

(28, 28+81, 97)-Net over F₈ — Digital

Digital (28, 109, 97)-net over F₈, using

net from sequence [i] based on digital (28, 96)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
  - a curve from the manYPoints database [i]

(28, 28+81, 593)-Net in Base 8 — Upper bound on s

There is no (28, 109, 594)-net in base 8, because

1 times m-reduction [i] would yield (28, 108, 594)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 36 080044 114582 873504 294166 157138 554996 944590 213961 839427 308306 476744 007956 761527 994018 016061 496820 > 8¹⁰⁸ [i]