MinT - Best Known (236−101, 236, s)-Nets in Base 3

Best Known (236−101, 236, s)-Nets in Base 3

(236−101, 236, 148)-Net over F₃ — Constructive and digital

Digital (135, 236, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 118, 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]

(236−101, 236, 179)-Net over F₃ — Digital

Digital (135, 236, 179)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−101, 236, 1653)-Net in Base 3 — Upper bound on s

There is no (135, 236, 1654)-net in base 3, because

1 times m-reduction [i] would yield (135, 235, 1654)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13427 630786 197047 541804 522071 678376 787841 787248 517173 658749 309194 452101 260284 087180 882815 422305 250984 924326 343661 > 3²³⁵ [i]