MinT - Best Known (54, 106, s)-Nets in Base 9

Best Known (54, 106, s)-Nets in Base 9

(54, 106, 200)-Net over F₉ — Constructive and digital

Digital (54, 106, 200)-net over F₉, using

trace code for nets [i] based on digital (1, 53, 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]

(54, 106, 225)-Net over F₉ — Digital

Digital (54, 106, 225)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 106, 10230)-Net in Base 9 — Upper bound on s

There is no (54, 106, 10231)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 141238 257575 585474 452379 579564 974735 096811 376223 745528 151747 545640 034401 924807 394793 453402 850484 807089 > 9¹⁰⁶ [i]