MinT - Best Known (188−82, 188, s)-Nets in Base 3

Best Known (188−82, 188, s)-Nets in Base 3

(188−82, 188, 80)-Net over F₃ — Constructive and digital

Digital (106, 188, 80)-net over F₃, using

8 times m-reduction [i] based on digital (106, 196, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 98, 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]

(188−82, 188, 139)-Net over F₃ — Digital

Digital (106, 188, 139)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−82, 188, 1203)-Net in Base 3 — Upper bound on s

There is no (106, 188, 1204)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 506821 080250 868562 760280 336369 761862 051375 435905 528113 490776 257899 170826 259337 362831 215977 > 3¹⁸⁸ [i]