MinT - Best Known (171−46, 171, s)-Nets in Base 3

Best Known (171−46, 171, s)-Nets in Base 3

(171−46, 171, 288)-Net over F₃ — Constructive and digital

Digital (125, 171, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 57, 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]

(171−46, 171, 565)-Net over F₃ — Digital

Digital (125, 171, 565)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−46, 171, 16600)-Net in Base 3 — Upper bound on s

There is no (125, 171, 16601)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3870 834307 907898 362045 193130 626730 976636 196504 712131 466838 384041 310401 881727 313067 > 3¹⁷¹ [i]