MinT - Best Known (124, 124+90, s)-Nets in Base 3

Best Known (124, 124+90, s)-Nets in Base 3

(124, 124+90, 148)-Net over F₃ — Constructive and digital

Digital (124, 214, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 107, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(124, 124+90, 172)-Net over F₃ — Digital

Digital (124, 214, 172)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 124+90, 1593)-Net in Base 3 — Upper bound on s

There is no (124, 214, 1594)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 296278 932986 353606 174795 894842 205852 137532 937295 699916 996022 326244 302642 283291 771209 044300 027465 343037 > 3²¹⁴ [i]