MinT - Best Known (216−66, 216, s)-Nets in Base 3

Best Known (216−66, 216, s)-Nets in Base 3

(216−66, 216, 228)-Net over F₃ — Constructive and digital

Digital (150, 216, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 72, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(216−66, 216, 447)-Net over F₃ — Digital

Digital (150, 216, 447)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−66, 216, 8703)-Net in Base 3 — Upper bound on s

There is no (150, 216, 8704)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 464585 488061 340383 333960 969223 373048 490590 227817 984375 295236 396750 826300 235539 112834 219334 346501 243905 > 3²¹⁶ [i]