MinT - Best Known (245−93, 245, s)-Nets in Base 3

Best Known (245−93, 245, s)-Nets in Base 3

(245−93, 245, 156)-Net over F₃ — Constructive and digital

Digital (152, 245, 156)-net over F₃, using

t-expansion [i] based on digital (147, 245, 156)-net over F₃, using
- 5 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]

(245−93, 245, 259)-Net over F₃ — Digital

Digital (152, 245, 259)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−93, 245, 3009)-Net in Base 3 — Upper bound on s

There is no (152, 245, 3010)-net in base 3, because

1 times m-reduction [i] would yield (152, 244, 3010)-net in base 3, but
- 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]