MinT - Best Known (235−101, 235, s)-Nets in Base 3

Best Known (235−101, 235, s)-Nets in Base 3

(235−101, 235, 128)-Net over F₃ — Constructive and digital

Digital (134, 235, 128)-net over F₃, using

7 times m-reduction [i] based on digital (134, 242, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 121, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(235−101, 235, 176)-Net over F₃ — Digital

Digital (134, 235, 176)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−101, 235, 1616)-Net in Base 3 — Upper bound on s

There is no (134, 235, 1617)-net in base 3, because

1 times m-reduction [i] would yield (134, 234, 1617)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4475 307299 873052 696076 413090 523898 770963 540369 147093 065380 727633 202526 923435 663913 592345 284899 212396 071276 364521 > 3²³⁴ [i]