MinT - Best Known (141−65, 141, s)-Nets in Base 9

Best Known (141−65, 141, s)-Nets in Base 9

(141−65, 141, 320)-Net over F₉ — Constructive and digital

Digital (76, 141, 320)-net over F₉, using

1 times m-reduction [i] based on digital (76, 142, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 71, 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]

(141−65, 141, 373)-Net over F₉ — Digital

Digital (76, 141, 373)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−65, 141, 23891)-Net in Base 9 — Upper bound on s

There is no (76, 141, 23892)-net in base 9, because

1 times m-reduction [i] would yield (76, 140, 23892)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 275649 248818 423217 521362 234608 931936 552895 052638 842749 127129 805634 531616 288392 533836 484352 398640 411959 263668 893779 395897 874111 007745 > 9¹⁴⁰ [i]