MinT - Best Known (207−64, 207, s)-Nets in Base 3

Best Known (207−64, 207, s)-Nets in Base 3

(207−64, 207, 204)-Net over F₃ — Constructive and digital

Digital (143, 207, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 69, 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]

(207−64, 207, 415)-Net over F₃ — Digital

Digital (143, 207, 415)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−64, 207, 7770)-Net in Base 3 — Upper bound on s

There is no (143, 207, 7771)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 580 997889 065004 934463 704916 868946 004489 099622 212999 786203 325852 381317 059129 077671 680837 047914 014657 > 3²⁰⁷ [i]