MinT - Best Known (126, 126+54, s)-Nets in Base 3

Best Known (126, 126+54, s)-Nets in Base 3

(126, 126+54, 228)-Net over F₃ — Constructive and digital

Digital (126, 180, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 60, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(126, 126+54, 405)-Net over F₃ — Digital

Digital (126, 180, 405)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+54, 8256)-Net in Base 3 — Upper bound on s

There is no (126, 180, 8257)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 304768 430926 437412 514776 018753 912462 905402 545486 406435 218672 806867 808728 687110 596283 > 3¹⁸⁰ [i]