MinT - Best Known (217−67, 217, s)-Nets in Base 3

Best Known (217−67, 217, s)-Nets in Base 3

(217−67, 217, 204)-Net over F₃ — Constructive and digital

Digital (150, 217, 204)-net over F₃, using

3¹ times duplication [i] based on digital (149, 216, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 72, 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]

(217−67, 217, 435)-Net over F₃ — Digital

Digital (150, 217, 435)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−67, 217, 8703)-Net in Base 3 — Upper bound on s

There is no (150, 217, 8704)-net in base 3, because

1 times m-reduction [i] would yield (150, 216, 8704)-net in base 3, but
- 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]