MinT - Best Known (76, 76+50, s)-Nets in Base 3

Best Known (76, 76+50, s)-Nets in Base 3

(76, 76+50, 128)-Net over F₃ — Constructive and digital

Digital (76, 126, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 63, 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]

(76, 76+50, 130)-Net over F₃ — Digital

Digital (76, 126, 130)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+50, 1267)-Net in Base 3 — Upper bound on s

There is no (76, 126, 1268)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 315992 389077 817452 571948 081243 508167 627239 778624 350370 189033 > 3¹²⁶ [i]