MinT - Best Known (90, 90+64, s)-Nets in Base 3

Best Known (90, 90+64, s)-Nets in Base 3

(90, 90+64, 128)-Net over F₃ — Constructive and digital

Digital (90, 154, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 77, 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]

(90, 90+64, 134)-Net over F₃ — Digital

Digital (90, 154, 134)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+64, 1233)-Net in Base 3 — Upper bound on s

There is no (90, 154, 1234)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30 312889 090143 352132 242761 864127 437893 550223 626466 896454 039223 006826 179905 > 3¹⁵⁴ [i]