MinT - Best Known (85, 85+55, s)-Nets in Base 9

Best Known (85, 85+55, s)-Nets in Base 9

(85, 85+55, 448)-Net over F₉ — Constructive and digital

Digital (85, 140, 448)-net over F₉, using

4 times m-reduction [i] based on digital (85, 144, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 72, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(85, 85+55, 791)-Net over F₉ — Digital

Digital (85, 140, 791)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+55, 111643)-Net in Base 9 — Upper bound on s

There is no (85, 140, 111644)-net in base 9, because

1 times m-reduction [i] would yield (85, 139, 111644)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 362364 979572 179361 155418 027657 106620 253137 336534 772451 085096 029529 263702 314355 435197 299952 459127 718136 807775 977887 578340 272847 575585 > 9¹³⁹ [i]