MinT - Best Known (189−84, 189, s)-Nets in Base 3

Best Known (189−84, 189, s)-Nets in Base 3

(189−84, 189, 80)-Net over F₃ — Constructive and digital

Digital (105, 189, 80)-net over F₃, using

5 times m-reduction [i] based on digital (105, 194, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 97, 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]

(189−84, 189, 132)-Net over F₃ — Digital

Digital (105, 189, 132)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(189−84, 189, 1117)-Net in Base 3 — Upper bound on s

There is no (105, 189, 1118)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 532437 483064 286428 662270 208252 100277 790498 329796 552554 127208 206616 649299 652471 806449 027085 > 3¹⁸⁹ [i]