MinT - Best Known (218−65, 218, s)-Nets in Base 3

Best Known (218−65, 218, s)-Nets in Base 3

(218−65, 218, 246)-Net over F₃ — Constructive and digital

Digital (153, 218, 246)-net over F₃, using

1 times m-reduction [i] based on digital (153, 219, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 73, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(218−65, 218, 487)-Net over F₃ — Digital

Digital (153, 218, 487)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(218−65, 218, 10966)-Net in Base 3 — Upper bound on s

There is no (153, 218, 10967)-net in base 3, because

1 times m-reduction [i] would yield (153, 217, 10967)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34 309251 970828 418583 910156 372799 936380 948113 971651 825175 114454 478052 762284 295155 848045 290463 851225 613761 > 3²¹⁷ [i]