MinT - Best Known (148−69, 148, s)-Nets in Base 9

Best Known (148−69, 148, s)-Nets in Base 9

(148−69, 148, 320)-Net over F₉ — Constructive and digital

Digital (79, 148, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 74, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(148−69, 148, 370)-Net over F₉ — Digital

Digital (79, 148, 370)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−69, 148, 22577)-Net in Base 9 — Upper bound on s

There is no (79, 148, 22578)-net in base 9, because

1 times m-reduction [i] would yield (79, 147, 22578)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 187 828498 536916 871881 568463 847663 482647 756584 881096 002749 192322 715920 510422 883080 904350 504377 608266 591777 485736 002801 603698 603972 395642 697697 > 9¹⁴⁷ [i]