MinT - Best Known (234−100, 234, s)-Nets in Base 3

Best Known (234−100, 234, s)-Nets in Base 3

(234−100, 234, 148)-Net over F₃ — Constructive and digital

Digital (134, 234, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 117, 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]

(234−100, 234, 178)-Net over F₃ — Digital

Digital (134, 234, 178)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−100, 234, 1616)-Net in Base 3 — Upper bound on s

There is no (134, 234, 1617)-net in base 3, because

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]