MinT - Best Known (106−79, 106, s)-Nets in Base 8

Best Known (106−79, 106, s)-Nets in Base 8

(106−79, 106, 65)-Net over F₈ — Constructive and digital

Digital (27, 106, 65)-net over F₈, using

t-expansion [i] based on digital (14, 106, 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]

(106−79, 106, 96)-Net over F₈ — Digital

Digital (27, 106, 96)-net over F₈, using

net from sequence [i] based on digital (27, 95)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 27 and N(F) ≥ 96, using
  - a curve from the manYPoints database [i]

(106−79, 106, 569)-Net in Base 8 — Upper bound on s

There is no (27, 106, 570)-net in base 8, because

1 times m-reduction [i] would yield (27, 105, 570)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 68313 676928 941667 323841 735901 619999 944950 331962 179069 934835 443863 654919 514836 589392 923460 668364 > 8¹⁰⁵ [i]