MinT - Best Known (107, 107+46, s)-Nets in Base 3

Best Known (107, 107+46, s)-Nets in Base 3

(107, 107+46, 204)-Net over F₃ — Constructive and digital

Digital (107, 153, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 51, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(107, 107+46, 351)-Net over F₃ — Digital

Digital (107, 153, 351)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+46, 7013)-Net in Base 3 — Upper bound on s

There is no (107, 153, 7014)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 008217 718939 483144 901430 596799 869353 743072 767719 317863 716199 249375 116025 > 3¹⁵³ [i]