MinT - Best Known (224−103, 224, s)-Nets in Base 3

Best Known (224−103, 224, s)-Nets in Base 3

(224−103, 224, 80)-Net over F₃ — Constructive and digital

Digital (121, 224, 80)-net over F₃, using

2 times m-reduction [i] based on digital (121, 226, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 113, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(224−103, 224, 140)-Net over F₃ — Digital

Digital (121, 224, 140)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−103, 224, 1161)-Net in Base 3 — Upper bound on s

There is no (121, 224, 1162)-net in base 3, because

1 times m-reduction [i] would yield (121, 223, 1162)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25940 090978 439783 517225 793865 064599 892894 669979 322857 288488 224386 839885 423903 392850 206651 546046 999903 427025 > 3²²³ [i]