MinT - Best Known (123, 123+79, s)-Nets in Base 3

Best Known (123, 123+79, s)-Nets in Base 3

(123, 123+79, 156)-Net over F₃ — Constructive and digital

Digital (123, 202, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 101, 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]

(123, 123+79, 201)-Net over F₃ — Digital

Digital (123, 202, 201)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+79, 2176)-Net in Base 3 — Upper bound on s

There is no (123, 202, 2177)-net in base 3, because

1 times m-reduction [i] would yield (123, 201, 2177)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 797751 283713 433250 077126 545882 169486 208041 372094 568876 601194 469771 983669 045023 049105 844533 434891 > 3²⁰¹ [i]