MinT - Best Known (138, 138+104, s)-Nets in Base 3

Best Known (138, 138+104, s)-Nets in Base 3

(138, 138+104, 148)-Net over F₃ — Constructive and digital

Digital (138, 242, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 121, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(138, 138+104, 181)-Net over F₃ — Digital

Digital (138, 242, 181)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138, 138+104, 1629)-Net in Base 3 — Upper bound on s

There is no (138, 242, 1630)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 816300 442626 820984 569639 700626 978567 965139 066764 888477 047084 212980 039718 266322 138945 335369 653340 178459 282926 664169 > 3²⁴² [i]