MinT - Best Known (219−68, 219, s)-Nets in Base 3

Best Known (219−68, 219, s)-Nets in Base 3

(219−68, 219, 204)-Net over F₃ — Constructive and digital

Digital (151, 219, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 73, 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]

(219−68, 219, 431)-Net over F₃ — Digital

Digital (151, 219, 431)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−68, 219, 7977)-Net in Base 3 — Upper bound on s

There is no (151, 219, 7978)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 309 754835 636650 478747 410068 972646 612488 157075 536857 342764 903583 722331 307093 793158 986215 367909 492534 620677 > 3²¹⁹ [i]