MinT - Best Known (247−73, 247, s)-Nets in Base 3

Best Known (247−73, 247, s)-Nets in Base 3

(247−73, 247, 264)-Net over F₃ — Constructive and digital

Digital (174, 247, 264)-net over F₃, using

3¹ times duplication [i] based on digital (173, 246, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 82, 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]

(247−73, 247, 559)-Net over F₃ — Digital

Digital (174, 247, 559)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−73, 247, 12967)-Net in Base 3 — Upper bound on s

There is no (174, 247, 12968)-net in base 3, because

1 times m-reduction [i] would yield (174, 246, 12968)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2358 660994 081588 357918 941026 306615 705830 608024 951190 031419 032509 939585 634381 152812 076915 379736 859651 967531 476381 518401 > 3²⁴⁶ [i]