MinT - Best Known (162, 162+70, s)-Nets in Base 3

Best Known (162, 162+70, s)-Nets in Base 3

(162, 162+70, 246)-Net over F₃ — Constructive and digital

Digital (162, 232, 246)-net over F₃, using

3¹ times duplication [i] based on digital (161, 231, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 77, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(162, 162+70, 495)-Net over F₃ — Digital

Digital (162, 232, 495)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+70, 10078)-Net in Base 3 — Upper bound on s

There is no (162, 232, 10079)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 493 509144 723004 800951 424564 489454 358230 081961 934571 826019 542207 009495 445150 783930 667644 619014 459221 019911 707451 > 3²³² [i]