MinT - Best Known (106, 106+63, s)-Nets in Base 3

Best Known (106, 106+63, s)-Nets in Base 3

(106, 106+63, 148)-Net over F₃ — Constructive and digital

Digital (106, 169, 148)-net over F₃, using

9 times m-reduction [i] based on digital (106, 178, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 89, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(106, 106+63, 198)-Net over F₃ — Digital

Digital (106, 169, 198)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+63, 2361)-Net in Base 3 — Upper bound on s

There is no (106, 169, 2362)-net in base 3, because

1 times m-reduction [i] would yield (106, 168, 2362)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 144 680680 476734 419986 042294 981001 794783 387326 868741 607285 849014 173941 678534 520985 > 3¹⁶⁸ [i]