MinT - Best Known (124, 124+98, s)-Nets in Base 3

Best Known (124, 124+98, s)-Nets in Base 3

(124, 124+98, 128)-Net over F₃ — Constructive and digital

Digital (124, 222, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 111, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(124, 124+98, 155)-Net over F₃ — Digital

Digital (124, 222, 155)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+98, 1338)-Net in Base 3 — Upper bound on s

There is no (124, 222, 1339)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8416 500406 772071 795181 821459 467129 916081 822661 393958 928553 577860 915234 663025 393902 741261 256161 387212 144023 > 3²²² [i]