MinT - Best Known (133, 133+50, s)-Nets in Base 3

Best Known (133, 133+50, s)-Nets in Base 3

(133, 133+50, 288)-Net over F₃ — Constructive and digital

Digital (133, 183, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 61, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(133, 133+50, 565)-Net over F₃ — Digital

Digital (133, 183, 565)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133, 133+50, 15792)-Net in Base 3 — Upper bound on s

There is no (133, 183, 15793)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2058 445666 510267 686167 975009 624333 566307 746830 993192 119946 273685 380571 023768 760782 143235 > 3¹⁸³ [i]