MinT - Best Known (217−63, 217, s)-Nets in Base 3

Best Known (217−63, 217, s)-Nets in Base 3

(217−63, 217, 264)-Net over F₃ — Constructive and digital

Digital (154, 217, 264)-net over F₃, using

3¹ times duplication [i] based on digital (153, 216, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 72, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(217−63, 217, 529)-Net over F₃ — Digital

Digital (154, 217, 529)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−63, 217, 13075)-Net in Base 3 — Upper bound on s

There is no (154, 217, 13076)-net in base 3, because

1 times m-reduction [i] would yield (154, 216, 13076)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 454242 042995 856825 060380 264762 398179 971651 097900 553561 681095 069677 512912 713436 656605 844046 832223 894641 > 3²¹⁶ [i]