MinT - Best Known (244−95, 244, s)-Nets in Base 3

Best Known (244−95, 244, s)-Nets in Base 3

(244−95, 244, 156)-Net over F₃ — Constructive and digital

Digital (149, 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]

(244−95, 244, 240)-Net over F₃ — Digital

Digital (149, 244, 240)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−95, 244, 2644)-Net in Base 3 — Upper bound on s

There is no (149, 244, 2645)-net in base 3, because

1 times m-reduction [i] would yield (149, 243, 2645)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 691843 738527 132889 160094 674648 892248 748074 905685 089511 459348 595962 214555 507409 107998 281244 153946 221364 667441 584699 > 3²⁴³ [i]