MinT - Best Known (158−98, 158, s)-Nets in Base 3

Best Known (158−98, 158, s)-Nets in Base 3

(158−98, 158, 48)-Net over F₃ — Constructive and digital

Digital (60, 158, 48)-net over F₃, using

t-expansion [i] based on digital (45, 158, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(158−98, 158, 64)-Net over F₃ — Digital

Digital (60, 158, 64)-net over F₃, using

t-expansion [i] based on digital (49, 158, 64)-net over F₃, using
- net from sequence [i] based on digital (49, 63)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
    - a curve from the manYPoints database [i]

(158−98, 158, 284)-Net in Base 3 — Upper bound on s

There is no (60, 158, 285)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2642 435587 676250 708566 957853 970997 554753 685255 872001 560825 088162 267819 246715 > 3¹⁵⁸ [i]