MinT - Best Known (121−51, 121, s)-Nets in Base 9

Best Known (121−51, 121, s)-Nets in Base 9

(121−51, 121, 344)-Net over F₉ — Constructive and digital

Digital (70, 121, 344)-net over F₉, using

5 times m-reduction [i] based on digital (70, 126, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 63, 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]

(121−51, 121, 494)-Net over F₉ — Digital

Digital (70, 121, 494)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−51, 121, 48390)-Net in Base 9 — Upper bound on s

There is no (70, 121, 48391)-net in base 9, because

1 times m-reduction [i] would yield (70, 120, 48391)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 229324 064518 271012 180725 198061 578897 509464 764467 364731 427852 508936 651372 749594 228310 619236 819737 468325 620942 569849 > 9¹²⁰ [i]