MinT - Best Known (124, 202, s)-Nets in Base 3

Best Known (124, 202, s)-Nets in Base 3

(124, 202, 156)-Net over F₃ — Constructive and digital

Digital (124, 202, 156)-net over F₃, using

2 times m-reduction [i] based on digital (124, 204, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 102, 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]

(124, 202, 208)-Net over F₃ — Digital

Digital (124, 202, 208)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 202, 2240)-Net in Base 3 — Upper bound on s

There is no (124, 202, 2241)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 422869 156525 015096 805678 588754 650092 873148 353855 363123 064537 096568 648382 040093 418351 901956 119307 > 3²⁰² [i]