MinT - Best Known (210−92, 210, s)-Nets in Base 3

Best Known (210−92, 210, s)-Nets in Base 3

(210−92, 210, 128)-Net over F₃ — Constructive and digital

Digital (118, 210, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 105, 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]

(210−92, 210, 151)-Net over F₃ — Digital

Digital (118, 210, 151)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−92, 210, 1311)-Net in Base 3 — Upper bound on s

There is no (118, 210, 1312)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15982 395565 946474 588945 981263 425640 313110 108212 925097 223946 242434 311973 989771 363541 867277 525076 754625 > 3²¹⁰ [i]