MinT - Best Known (70, 70+57, s)-Nets in Base 9

Best Known (70, 70+57, s)-Nets in Base 9

(70, 70+57, 320)-Net over F₉ — Constructive and digital

Digital (70, 127, 320)-net over F₉, using

3 times m-reduction [i] based on digital (70, 130, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 65, 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]

(70, 70+57, 384)-Net over F₉ — Digital

Digital (70, 127, 384)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+57, 27780)-Net in Base 9 — Upper bound on s

There is no (70, 127, 27781)-net in base 9, because

1 times m-reduction [i] would yield (70, 126, 27781)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 716946 964666 757297 741676 264630 579945 704539 599055 285662 117216 328045 692488 334684 453954 644464 693806 748647 857069 478374 229473 > 9¹²⁶ [i]