MinT - Best Known (244−71, 244, s)-Nets in Base 3

Best Known (244−71, 244, s)-Nets in Base 3

(244−71, 244, 282)-Net over F₃ — Constructive and digital

Digital (173, 244, 282)-net over F₃, using

3¹ times duplication [i] based on digital (172, 243, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 81, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(244−71, 244, 582)-Net over F₃ — Digital

Digital (173, 244, 582)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−71, 244, 14248)-Net in Base 3 — Upper bound on s

There is no (173, 244, 14249)-net in base 3, because

1 times m-reduction [i] would yield (173, 243, 14249)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 295643 907893 152396 114473 314273 415244 517276 821118 048771 953471 615819 077495 089727 454312 964639 779235 837398 539892 174971 > 3²⁴³ [i]