MinT - Best Known (208−65, 208, s)-Nets in Base 3

Best Known (208−65, 208, s)-Nets in Base 3

(208−65, 208, 192)-Net over F₃ — Constructive and digital

Digital (143, 208, 192)-net over F₃, using

3¹ times duplication [i] based on digital (142, 207, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 69, 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]

(208−65, 208, 403)-Net over F₃ — Digital

Digital (143, 208, 403)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(208−65, 208, 7770)-Net in Base 3 — Upper bound on s

There is no (143, 208, 7771)-net in base 3, because

1 times m-reduction [i] would yield (143, 207, 7771)-net in base 3, but
- 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]