MinT - Best Known (78, 78+43, s)-Nets in Base 9

Best Known (78, 78+43, s)-Nets in Base 9

(78, 78+43, 740)-Net over F₉ — Constructive and digital

Digital (78, 121, 740)-net over F₉, using

3 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+43, 1179)-Net over F₉ — Digital

Digital (78, 121, 1179)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+43, 307750)-Net in Base 9 — Upper bound on s

There is no (78, 121, 307751)-net in base 9, because

1 times m-reduction [i] would yield (78, 120, 307751)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 229303 570673 320490 037699 446964 087242 283620 856954 575222 826419 636342 702431 731909 860897 872476 273329 757222 312498 368409 > 9¹²⁰ [i]