MinT - Best Known (144, 144+48, s)-Nets in Base 3

Best Known (144, 144+48, s)-Nets in Base 3

(144, 144+48, 328)-Net over F₃ — Constructive and digital

Digital (144, 192, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 48, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(144, 144+48, 822)-Net over F₃ — Digital

Digital (144, 192, 822)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(144, 144+48, 32135)-Net in Base 3 — Upper bound on s

There is no (144, 192, 32136)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 498115 020485 831362 520184 723983 053239 815413 368541 831135 605793 604949 262211 769522 134015 481089 > 3¹⁹² [i]