MinT - Best Known (122−49, 122, s)-Nets in Base 9

Best Known (122−49, 122, s)-Nets in Base 9

(122−49, 122, 344)-Net over F₉ — Constructive and digital

Digital (73, 122, 344)-net over F₉, using

10 times m-reduction [i] based on digital (73, 132, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 66, 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]

(122−49, 122, 633)-Net over F₉ — Digital

Digital (73, 122, 633)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−49, 122, 79280)-Net in Base 9 — Upper bound on s

There is no (73, 122, 79281)-net in base 9, because

1 times m-reduction [i] would yield (73, 121, 79281)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29 068252 197640 712231 630299 802826 437217 445619 484599 651160 579896 987644 024718 834011 596568 953892 503888 623013 945717 268929 > 9¹²¹ [i]