MinT - Best Known (108−79, 108, s)-Nets in Base 8

Best Known (108−79, 108, s)-Nets in Base 8

(108−79, 108, 65)-Net over F₈ — Constructive and digital

Digital (29, 108, 65)-net over F₈, using

t-expansion [i] based on digital (14, 108, 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]

(108−79, 108, 97)-Net over F₈ — Digital

Digital (29, 108, 97)-net over F₈, using

t-expansion [i] based on digital (28, 108, 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]

(108−79, 108, 636)-Net in Base 8 — Upper bound on s

There is no (29, 108, 637)-net in base 8, because

1 times m-reduction [i] would yield (29, 107, 637)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 412686 068808 102778 655753 083336 149541 004294 887880 202371 067480 246002 938731 004368 807878 039757 829592 > 8¹⁰⁷ [i]