MinT - Best Known (133−61, 133, s)-Nets in Base 9

Best Known (133−61, 133, s)-Nets in Base 9

(133−61, 133, 320)-Net over F₉ — Constructive and digital

Digital (72, 133, 320)-net over F₉, using

1 times m-reduction [i] based on digital (72, 134, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 67, 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]

(133−61, 133, 362)-Net over F₉ — Digital

Digital (72, 133, 362)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−61, 133, 23770)-Net in Base 9 — Upper bound on s

There is no (72, 133, 23771)-net in base 9, because

1 times m-reduction [i] would yield (72, 132, 23771)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 912976 868840 033998 225267 189043 046999 358080 627849 268775 088540 766682 900094 144014 765641 079521 185782 948670 052267 665001 444846 336209 > 9¹³² [i]