MinT - Best Known (126, 226, s)-Nets in Base 3

Best Known (126, 226, s)-Nets in Base 3

(126, 226, 128)-Net over F₃ — Constructive and digital

Digital (126, 226, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 113, 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]

(126, 226, 157)-Net over F₃ — Digital

Digital (126, 226, 157)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 226, 1348)-Net in Base 3 — Upper bound on s

There is no (126, 226, 1349)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 692482 516907 068886 528408 783811 451177 606229 076528 326912 882173 490941 364197 839432 683195 250145 151122 423247 735697 > 3²²⁶ [i]