MinT - Best Known (242−99, 242, s)-Nets in Base 3

Best Known (242−99, 242, s)-Nets in Base 3

(242−99, 242, 156)-Net over F₃ — Constructive and digital

Digital (143, 242, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 121, 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]

(242−99, 242, 207)-Net over F₃ — Digital

Digital (143, 242, 207)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−99, 242, 2074)-Net in Base 3 — Upper bound on s

There is no (143, 242, 2075)-net in base 3, because

1 times m-reduction [i] would yield (143, 241, 2075)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 712928 310091 704948 543763 454030 823745 675368 697347 865182 441732 996354 582472 480234 815222 171886 434867 296543 385465 056087 > 3²⁴¹ [i]