MinT - Best Known (171−53, 171, s)-Nets in Base 3

Best Known (171−53, 171, s)-Nets in Base 3

(171−53, 171, 192)-Net over F₃ — Constructive and digital

Digital (118, 171, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 57, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(171−53, 171, 349)-Net over F₃ — Digital

Digital (118, 171, 349)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−53, 171, 6923)-Net in Base 3 — Upper bound on s

There is no (118, 171, 6924)-net in base 3, because

1 times m-reduction [i] would yield (118, 170, 6924)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1293 867982 526559 870839 363814 890446 276428 497421 820718 967865 717626 149412 551338 740585 > 3¹⁷⁰ [i]