MinT - Best Known (135, 135+97, s)-Nets in Base 3

Best Known (135, 135+97, s)-Nets in Base 3

(135, 135+97, 148)-Net over F₃ — Constructive and digital

Digital (135, 232, 148)-net over F₃, using

4 times m-reduction [i] based on digital (135, 236, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 118, 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]

(135, 135+97, 188)-Net over F₃ — Digital

Digital (135, 232, 188)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+97, 1806)-Net in Base 3 — Upper bound on s

There is no (135, 232, 1807)-net in base 3, because

1 times m-reduction [i] would yield (135, 231, 1807)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 167 799276 602521 975283 407492 077559 249530 087650 544639 554890 966856 351447 786304 303723 574687 443558 885970 486179 674529 > 3²³¹ [i]