MinT - Best Known (151, 151+98, s)-Nets in Base 3

Best Known (151, 151+98, s)-Nets in Base 3

(151, 151+98, 156)-Net over F₃ — Constructive and digital

Digital (151, 249, 156)-net over F₃, using

t-expansion [i] based on digital (147, 249, 156)-net over F₃, using
- 1 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]

(151, 151+98, 237)-Net over F₃ — Digital

Digital (151, 249, 237)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+98, 2491)-Net in Base 3 — Upper bound on s

There is no (151, 249, 2492)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63709 227604 948089 452475 838973 392437 045109 753995 286447 551237 424251 112144 275108 444686 940601 777755 401139 053009 141523 219321 > 3²⁴⁹ [i]