MinT - Best Known (185−61, 185, s)-Nets in Base 3

Best Known (185−61, 185, s)-Nets in Base 3

(185−61, 185, 156)-Net over F₃ — Constructive and digital

Digital (124, 185, 156)-net over F₃, using

19 times m-reduction [i] based on digital (124, 204, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 102, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(185−61, 185, 308)-Net over F₃ — Digital

Digital (124, 185, 308)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−61, 185, 5053)-Net in Base 3 — Upper bound on s

There is no (124, 185, 5054)-net in base 3, because

1 times m-reduction [i] would yield (124, 184, 5054)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6193 581496 446059 641268 931466 144839 412778 776171 239112 901643 180248 091071 222421 343973 859541 > 3¹⁸⁴ [i]