MinT - Best Known (194−72, 194, s)-Nets in Base 3

Best Known (194−72, 194, s)-Nets in Base 3

(194−72, 194, 156)-Net over F₃ — Constructive and digital

Digital (122, 194, 156)-net over F₃, using

6 times m-reduction [i] based on digital (122, 200, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 100, 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]

(194−72, 194, 225)-Net over F₃ — Digital

Digital (122, 194, 225)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−72, 194, 2624)-Net in Base 3 — Upper bound on s

There is no (122, 194, 2625)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 366 494929 542274 351358 780050 836473 263614 826788 051451 253752 408474 680659 514238 214440 321504 663761 > 3¹⁹⁴ [i]