MinT - Best Known (197−73, 197, s)-Nets in Base 3

Best Known (197−73, 197, s)-Nets in Base 3

(197−73, 197, 156)-Net over F₃ — Constructive and digital

Digital (124, 197, 156)-net over F₃, using

7 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]

(197−73, 197, 230)-Net over F₃ — Digital

Digital (124, 197, 230)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−73, 197, 2791)-Net in Base 3 — Upper bound on s

There is no (124, 197, 2792)-net in base 3, because

1 times m-reduction [i] would yield (124, 196, 2792)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3281 077256 386577 469076 389898 884388 581680 374507 835972 169259 077036 702494 550204 894261 981196 329025 > 3¹⁹⁶ [i]