MinT - Best Known (193−87, 193, s)-Nets in Base 3

Best Known (193−87, 193, s)-Nets in Base 3

(193−87, 193, 80)-Net over F₃ — Constructive and digital

Digital (106, 193, 80)-net over F₃, using

3 times m-reduction [i] based on digital (106, 196, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 98, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(193−87, 193, 130)-Net over F₃ — Digital

Digital (106, 193, 130)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−87, 193, 1097)-Net in Base 3 — Upper bound on s

There is no (106, 193, 1098)-net in base 3, because

1 times m-reduction [i] would yield (106, 192, 1098)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 516110 724040 517501 706340 400876 943053 720231 183833 915148 352478 749155 495240 396796 210939 495969 > 3¹⁹² [i]