MinT - Best Known (159−41, 159, s)-Nets in Base 3

Best Known (159−41, 159, s)-Nets in Base 3

(159−41, 159, 288)-Net over F₃ — Constructive and digital

Digital (118, 159, 288)-net over F₃, using

t-expansion [i] based on digital (117, 159, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 53, 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]

(159−41, 159, 627)-Net over F₃ — Digital

Digital (118, 159, 627)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−41, 159, 24388)-Net in Base 3 — Upper bound on s

There is no (118, 159, 24389)-net in base 3, because

1 times m-reduction [i] would yield (118, 158, 24389)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2428 257839 927784 031129 355311 194665 875742 087739 752846 870309 379080 024752 352529 > 3¹⁵⁸ [i]