MinT - Best Known (72, 118, s)-Nets in Base 3

Best Known (72, 118, s)-Nets in Base 3

(72, 118, 128)-Net over F₃ — Constructive and digital

Digital (72, 118, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 59, 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]

(72, 118, 129)-Net over F₃ — Digital

Digital (72, 118, 129)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 118, 1299)-Net in Base 3 — Upper bound on s

There is no (72, 118, 1300)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 200 492381 917521 813812 747715 829929 920418 431268 377928 415281 > 3¹¹⁸ [i]