MinT - Best Known (226−91, 226, s)-Nets in Base 3

Best Known (226−91, 226, s)-Nets in Base 3

(226−91, 226, 156)-Net over F₃ — Constructive and digital

Digital (135, 226, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 113, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(226−91, 226, 204)-Net over F₃ — Digital

Digital (135, 226, 204)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−91, 226, 2097)-Net in Base 3 — Upper bound on s

There is no (135, 226, 2098)-net in base 3, because

1 times m-reduction [i] would yield (135, 225, 2098)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 227245 660357 366629 454287 156511 799165 981842 398455 033942 632132 641536 246153 838053 121768 233964 522150 993808 729069 > 3²²⁵ [i]