MinT - Best Known (245−95, 245, s)-Nets in Base 3

Best Known (245−95, 245, s)-Nets in Base 3

(245−95, 245, 156)-Net over F₃ — Constructive and digital

Digital (150, 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]

(245−95, 245, 244)-Net over F₃ — Digital

Digital (150, 245, 244)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−95, 245, 2708)-Net in Base 3 — Upper bound on s

There is no (150, 245, 2709)-net in base 3, because

1 times m-reduction [i] would yield (150, 244, 2709)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 264 702353 176407 327414 038984 180962 646362 616392 833743 511564 724824 970799 074020 898057 637796 898919 859370 896514 530501 659451 > 3²⁴⁴ [i]