MinT - Best Known (212−48, 212, s)-Nets in Base 3

Best Known (212−48, 212, s)-Nets in Base 3

(212−48, 212, 640)-Net over F₃ — Constructive and digital

Digital (164, 212, 640)-net over F₃, using

trace code for nets [i] based on digital (5, 53, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(212−48, 212, 1327)-Net over F₃ — Digital

Digital (164, 212, 1327)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−48, 212, 80311)-Net in Base 3 — Upper bound on s

There is no (164, 212, 80312)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 141186 729321 826122 293033 579045 367854 800200 200744 786864 772073 941197 083251 517470 423707 358878 972769 934593 > 3²¹² [i]