MinT - Best Known (106−41, 106, s)-Nets in Base 9

Best Known (106−41, 106, s)-Nets in Base 9

(106−41, 106, 344)-Net over F₉ — Constructive and digital

Digital (65, 106, 344)-net over F₉, using

10 times m-reduction [i] based on digital (65, 116, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 58, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(106−41, 106, 686)-Net over F₉ — Digital

Digital (65, 106, 686)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−41, 106, 106154)-Net in Base 9 — Upper bound on s

There is no (65, 106, 106155)-net in base 9, because

1 times m-reduction [i] would yield (65, 105, 106155)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15684 331027 986194 057763 629656 628884 111887 860288 578603 558291 385258 368800 503290 914245 480264 685279 826401 > 9¹⁰⁵ [i]