MinT - Best Known (146, 146+104, s)-Nets in Base 3

Best Known (146, 146+104, s)-Nets in Base 3

(146, 146+104, 148)-Net over F₃ — Constructive and digital

Digital (146, 250, 148)-net over F₃, using

t-expansion [i] based on digital (142, 250, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 125, 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]

(146, 146+104, 204)-Net over F₃ — Digital

Digital (146, 250, 204)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 146+104, 1938)-Net in Base 3 — Upper bound on s

There is no (146, 250, 1939)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193519 353275 150451 479830 028045 012138 823447 789041 942778 107856 649084 414652 487752 199653 839052 659072 640133 840101 381189 036409 > 3²⁵⁰ [i]