MinT - Best Known (121, 171, s)-Nets in Base 3

Best Known (121, 171, s)-Nets in Base 3

(121, 171, 246)-Net over F₃ — Constructive and digital

Digital (121, 171, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 57, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(121, 171, 422)-Net over F₃ — Digital

Digital (121, 171, 422)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(121, 171, 9310)-Net in Base 3 — Upper bound on s

There is no (121, 171, 9311)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3877 149710 822159 052020 644756 067551 298140 138187 621775 694072 835667 310229 680549 571727 > 3¹⁷¹ [i]