MinT - Best Known (67, 67+57, s)-Nets in Base 9

Best Known (67, 67+57, s)-Nets in Base 9

(67, 67+57, 320)-Net over F₉ — Constructive and digital

Digital (67, 124, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 62, 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]

(67, 67+57, 338)-Net over F₉ — Digital

Digital (67, 124, 338)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+57, 21949)-Net in Base 9 — Upper bound on s

There is no (67, 124, 21950)-net in base 9, because

1 times m-reduction [i] would yield (67, 123, 21950)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2354 819661 300179 770860 838016 096459 001482 421330 894751 787817 899603 216253 168334 888745 832067 242529 954497 923312 993301 517505 > 9¹²³ [i]