MinT - Best Known (171, 171+61, s)-Nets in Base 3

Best Known (171, 171+61, s)-Nets in Base 3

(171, 171+61, 288)-Net over F₃ — Constructive and digital

Digital (171, 232, 288)-net over F₃, using

8 times m-reduction [i] based on digital (171, 240, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 80, 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, 171+61, 793)-Net over F₃ — Digital

Digital (171, 232, 793)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+61, 28388)-Net in Base 3 — Upper bound on s

There is no (171, 232, 28389)-net in base 3, because

1 times m-reduction [i] would yield (171, 231, 28389)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 164 160422 846513 105353 783146 819424 454555 242180 762870 219368 994847 488273 118771 085124 851567 607143 277767 696401 126241 > 3²³¹ [i]