MinT - Best Known (218−64, 218, s)-Nets in Base 3

Best Known (218−64, 218, s)-Nets in Base 3

(218−64, 218, 252)-Net over F₃ — Constructive and digital

Digital (154, 218, 252)-net over F₃, using

1 times m-reduction [i] based on digital (154, 219, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 73, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(218−64, 218, 512)-Net over F₃ — Digital

Digital (154, 218, 512)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−64, 218, 11351)-Net in Base 3 — Upper bound on s

There is no (154, 218, 11352)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 103 173864 307991 960712 259654 307196 670575 704374 231634 769319 768554 597176 228872 482233 768078 211385 920090 847233 > 3²¹⁸ [i]