MinT - Best Known (244−91, 244, s)-Nets in Base 3

Best Known (244−91, 244, s)-Nets in Base 3

(244−91, 244, 156)-Net over F₃ — Constructive and digital

Digital (153, 244, 156)-net over F₃, using

t-expansion [i] based on digital (147, 244, 156)-net over F₃, using
- 6 times m-reduction [i] based on digital (147, 250, 156)-net over F₃, using
  - trace code for nets [i] based on digital (22, 125, 78)-net over F₉, using
    - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
        F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(244−91, 244, 272)-Net over F₃ — Digital

Digital (153, 244, 272)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−91, 244, 3279)-Net in Base 3 — Upper bound on s

There is no (153, 244, 3280)-net in base 3, because

1 times m-reduction [i] would yield (153, 243, 3280)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88 058662 443889 309396 508471 760573 826891 234867 086598 163758 516536 433114 306796 848003 005519 742297 145989 580575 889294 846625 > 3²⁴³ [i]