MinT - Best Known (128−35, 128, s)-Nets in Base 3

Best Known (128−35, 128, s)-Nets in Base 3

(128−35, 128, 246)-Net over F₃ — Constructive and digital

Digital (93, 128, 246)-net over F₃, using

1 times m-reduction [i] based on digital (93, 129, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 43, 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]

(128−35, 128, 424)-Net over F₃ — Digital

Digital (93, 128, 424)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−35, 128, 13144)-Net in Base 3 — Upper bound on s

There is no (93, 128, 13145)-net in base 3, because

1 times m-reduction [i] would yield (93, 127, 13145)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 932132 588408 931058 063942 714405 256057 283459 882776 636592 070515 > 3¹²⁷ [i]