MinT - Best Known (222−102, 222, s)-Nets in Base 3

Best Known (222−102, 222, s)-Nets in Base 3

(222−102, 222, 80)-Net over F₃ — Constructive and digital

Digital (120, 222, 80)-net over F₃, using

2 times m-reduction [i] based on digital (120, 224, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 112, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(222−102, 222, 139)-Net over F₃ — Digital

Digital (120, 222, 139)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−102, 222, 1135)-Net in Base 3 — Upper bound on s

There is no (120, 222, 1136)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8573 731471 966573 050141 783811 803668 225530 772914 254044 649137 663594 254090 265614 522361 815490 491168 851325 232577 > 3²²² [i]