MinT - Best Known (246−71, 246, s)-Nets in Base 3

Best Known (246−71, 246, s)-Nets in Base 3

(246−71, 246, 288)-Net over F₃ — Constructive and digital

Digital (175, 246, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 82, 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]

(246−71, 246, 602)-Net over F₃ — Digital

Digital (175, 246, 602)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−71, 246, 15173)-Net in Base 3 — Upper bound on s

There is no (175, 246, 15174)-net in base 3, because

1 times m-reduction [i] would yield (175, 245, 15174)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 784 888449 589208 545170 226469 019765 097369 120678 640210 240816 269033 651928 160426 960194 893946 823060 187166 764761 413690 789025 > 3²⁴⁵ [i]