MinT - Best Known (121, 121+90, s)-Nets in Base 3

Best Known (121, 121+90, s)-Nets in Base 3

(121, 121+90, 128)-Net over F₃ — Constructive and digital

Digital (121, 211, 128)-net over F₃, using

5 times m-reduction [i] based on digital (121, 216, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 108, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(121, 121+90, 164)-Net over F₃ — Digital

Digital (121, 211, 164)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 121+90, 1477)-Net in Base 3 — Upper bound on s

There is no (121, 211, 1478)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 47506 869902 741392 718394 421802 758621 627674 711521 677990 624238 939386 997782 389174 509511 241737 396214 179861 > 3²¹¹ [i]