MinT - Best Known (108, 108+91, s)-Nets in Base 3

Best Known (108, 108+91, s)-Nets in Base 3

(108, 108+91, 80)-Net over F₃ — Constructive and digital

Digital (108, 199, 80)-net over F₃, using

1 times m-reduction [i] based on digital (108, 200, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 100, 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]

(108, 108+91, 128)-Net over F₃ — Digital

Digital (108, 199, 128)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+91, 1064)-Net in Base 3 — Upper bound on s

There is no (108, 199, 1065)-net in base 3, because

1 times m-reduction [i] would yield (108, 198, 1065)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30649 291569 929837 322282 660333 447282 532327 906126 154749 153998 227802 378856 045909 912966 375922 850723 > 3¹⁹⁸ [i]