MinT - Best Known (244−92, 244, s)-Nets in Base 3

Best Known (244−92, 244, s)-Nets in Base 3

(244−92, 244, 156)-Net over F₃ — Constructive and digital

Digital (152, 244, 156)-net over F₃, using

t-expansion [i] based on digital (147, 244, 156)-net over F₃, using
- 6 times m-reduction [i] based on digital (147, 250, 156)-net over F₃, using
  - trace code for nets [i] based on digital (22, 125, 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]

(244−92, 244, 263)-Net over F₃ — Digital

Digital (152, 244, 263)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(244−92, 244, 3009)-Net in Base 3 — Upper bound on s

There is no (152, 244, 3010)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 262 277607 602168 207207 222893 006783 907289 600020 293612 642962 573181 781501 090664 345233 332265 895549 548569 666167 843341 668941 > 3²⁴⁴ [i]