MinT - Best Known (78, 78+33, s)-Nets in Base 9

Best Known (78, 78+33, s)-Nets in Base 9

(78, 78+33, 740)-Net over F₉ — Constructive and digital

Digital (78, 111, 740)-net over F₉, using

13 times m-reduction [i] based on digital (78, 124, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 62, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(78, 78+33, 3280)-Net over F₉ — Digital

Digital (78, 111, 3280)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+33, 3089332)-Net in Base 9 — Upper bound on s

There is no (78, 111, 3089333)-net in base 9, because

1 times m-reduction [i] would yield (78, 110, 3089333)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 926 141068 032888 325360 730736 646908 085351 397379 220377 231191 448558 701276 877132 287098 701889 730293 515733 871745 > 9¹¹⁰ [i]