MinT - Best Known (60, 60+60, s)-Nets in Base 9

Best Known (60, 60+60, s)-Nets in Base 9

(60, 60+60, 164)-Net over F₉ — Constructive and digital

Digital (60, 120, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 60, 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]

(60, 60+60, 229)-Net over F₉ — Digital

Digital (60, 120, 229)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+60, 9859)-Net in Base 9 — Upper bound on s

There is no (60, 120, 9860)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 231668 236720 417016 671492 987701 760821 483293 627879 957346 093817 369257 164624 369429 837925 896835 422170 192296 562570 697537 > 9¹²⁰ [i]