MinT - Best Known (242−93, 242, s)-Nets in Base 3

Best Known (242−93, 242, s)-Nets in Base 3

(242−93, 242, 156)-Net over F₃ — Constructive and digital

Digital (149, 242, 156)-net over F₃, using

t-expansion [i] based on digital (147, 242, 156)-net over F₃, using
- 8 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]

(242−93, 242, 247)-Net over F₃ — Digital

Digital (149, 242, 247)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−93, 242, 2798)-Net in Base 3 — Upper bound on s

There is no (149, 242, 2799)-net in base 3, because

1 times m-reduction [i] would yield (149, 241, 2799)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 749182 413186 681334 509226 698542 550729 185768 897575 357175 213638 222145 497123 627439 747733 712408 176750 427432 091024 396805 > 3²⁴¹ [i]