MinT - Best Known (170−72, 170, s)-Nets in Base 3

Best Known (170−72, 170, s)-Nets in Base 3

(170−72, 170, 128)-Net over F₃ — Constructive and digital

Digital (98, 170, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 85, 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]

(170−72, 170, 138)-Net over F₃ — Digital

Digital (98, 170, 138)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−72, 170, 1243)-Net in Base 3 — Upper bound on s

There is no (98, 170, 1244)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1303 295621 313245 582810 194589 188821 371903 420678 705518 634063 045689 888058 504825 288193 > 3¹⁷⁰ [i]