MinT - Best Known (162−43, 162, s)-Nets in Base 3

Best Known (162−43, 162, s)-Nets in Base 3

(162−43, 162, 288)-Net over F₃ — Constructive and digital

Digital (119, 162, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 54, 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]

(162−43, 162, 569)-Net over F₃ — Digital

Digital (119, 162, 569)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−43, 162, 19721)-Net in Base 3 — Upper bound on s

There is no (119, 162, 19722)-net in base 3, because

1 times m-reduction [i] would yield (119, 161, 19722)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65573 288750 199230 074915 400196 340293 463691 839265 859382 015087 191950 522710 381005 > 3¹⁶¹ [i]