MinT - Best Known (128, 128+97, s)-Nets in Base 3

Best Known (128, 128+97, s)-Nets in Base 3

(128, 128+97, 128)-Net over F₃ — Constructive and digital

Digital (128, 225, 128)-net over F₃, using

5 times m-reduction [i] based on digital (128, 230, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 115, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(128, 128+97, 168)-Net over F₃ — Digital

Digital (128, 225, 168)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+97, 1531)-Net in Base 3 — Upper bound on s

There is no (128, 225, 1532)-net in base 3, because

1 times m-reduction [i] would yield (128, 224, 1532)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75288 994230 992760 593546 444175 671193 423506 392102 061983 846134 761172 054912 190368 512608 670070 645420 629408 315265 > 3²²⁴ [i]