MinT - Best Known (146, 146+56, s)-Nets in Base 3

Best Known (146, 146+56, s)-Nets in Base 3

(146, 146+56, 288)-Net over F₃ — Constructive and digital

Digital (146, 202, 288)-net over F₃, using

3¹ times duplication [i] based on digital (145, 201, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 67, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(146, 146+56, 582)-Net over F₃ — Digital

Digital (146, 202, 582)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(146, 146+56, 15606)-Net in Base 3 — Upper bound on s

There is no (146, 202, 15607)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 393510 055408 190202 740545 633900 371856 982551 414792 495609 666189 451983 061709 556263 087147 636779 215561 > 3²⁰² [i]