MinT - Best Known (236−97, 236, s)-Nets in Base 3

Best Known (236−97, 236, s)-Nets in Base 3

(236−97, 236, 148)-Net over F₃ — Constructive and digital

Digital (139, 236, 148)-net over F₃, using

8 times m-reduction [i] based on digital (139, 244, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 122, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(236−97, 236, 200)-Net over F₃ — Digital

Digital (139, 236, 200)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−97, 236, 1983)-Net in Base 3 — Upper bound on s

There is no (139, 236, 1984)-net in base 3, because

1 times m-reduction [i] would yield (139, 235, 1984)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13367 253035 084864 198132 549934 338977 948900 149910 678813 005134 165096 153309 249338 058270 740116 612905 283088 497157 074945 > 3²³⁵ [i]