MinT - Best Known (145−71, 145, s)-Nets in Base 9

Best Known (145−71, 145, s)-Nets in Base 9

(145−71, 145, 200)-Net over F₉ — Constructive and digital

Digital (74, 145, 200)-net over F₉, using

1 times m-reduction [i] based on digital (74, 146, 200)-net over F₉, using
- trace code for nets [i] based on digital (1, 73, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(145−71, 145, 294)-Net over F₉ — Digital

Digital (74, 145, 294)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−71, 145, 14640)-Net in Base 9 — Upper bound on s

There is no (74, 145, 14641)-net in base 9, because

1 times m-reduction [i] would yield (74, 144, 14641)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 257666 924607 234200 449363 297335 096251 576695 361035 725377 535962 690156 259417 748222 259758 627176 008487 187415 499738 533491 323649 214309 909289 028185 > 9¹⁴⁴ [i]