MinT - Best Known (134, 134+52, s)-Nets in Base 3

Best Known (134, 134+52, s)-Nets in Base 3

(134, 134+52, 282)-Net over F₃ — Constructive and digital

Digital (134, 186, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 62, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(134, 134+52, 527)-Net over F₃ — Digital

Digital (134, 186, 527)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134, 134+52, 13636)-Net in Base 3 — Upper bound on s

There is no (134, 186, 13637)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 55581 335831 762589 932839 415010 736827 622819 220506 079449 709173 207302 853469 378659 747718 543025 > 3¹⁸⁶ [i]