MinT - Best Known (132, 132+98, s)-Nets in Base 3

Best Known (132, 132+98, s)-Nets in Base 3

(132, 132+98, 148)-Net over F₃ — Constructive and digital

Digital (132, 230, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 115, 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]

(132, 132+98, 177)-Net over F₃ — Digital

Digital (132, 230, 177)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 132+98, 1611)-Net in Base 3 — Upper bound on s

There is no (132, 230, 1612)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56 313428 087319 415717 165787 035373 796125 383029 881152 988212 282632 721808 031863 045563 837240 896144 396072 940180 738713 > 3²³⁰ [i]