MinT - Best Known (218−67, 218, s)-Nets in Base 3

Best Known (218−67, 218, s)-Nets in Base 3

(218−67, 218, 204)-Net over F₃ — Constructive and digital

Digital (151, 218, 204)-net over F₃, using

1 times m-reduction [i] based on 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]

(218−67, 218, 443)-Net over F₃ — Digital

Digital (151, 218, 443)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−67, 218, 8999)-Net in Base 3 — Upper bound on s

There is no (151, 218, 9000)-net in base 3, because

1 times m-reduction [i] would yield (151, 217, 9000)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34 426258 032088 763723 390608 766571 209414 178046 427719 210776 069047 034911 714656 299603 456798 410465 259575 715921 > 3²¹⁷ [i]