MinT - Best Known (105, 105+46, s)-Nets in Base 3

Best Known (105, 105+46, s)-Nets in Base 3

(105, 105+46, 192)-Net over F₃ — Constructive and digital

Digital (105, 151, 192)-net over F₃, using

3¹ times duplication [i] based on digital (104, 150, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 50, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(105, 105+46, 332)-Net over F₃ — Digital

Digital (105, 151, 332)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+46, 6372)-Net in Base 3 — Upper bound on s

There is no (105, 151, 6373)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 112390 922821 893684 803772 478940 871719 827214 671410 672872 443387 861343 913371 > 3¹⁵¹ [i]