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

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

(61, 61+61, 164)-Net over F₉ — Constructive and digital

Digital (61, 122, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 61, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(61, 61+61, 233)-Net over F₉ — Digital

Digital (61, 122, 233)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+61, 10610)-Net in Base 9 — Upper bound on s

There is no (61, 122, 10611)-net in base 9, because

1 times m-reduction [i] would yield (61, 121, 10611)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29 114331 460761 565825 525422 255580 711280 255199 468536 757360 533586 760369 231803 278001 038678 319047 813474 623288 665028 447825 > 9¹²¹ [i]