MinT - Best Known (246−65, 246, s)-Nets in Base 3

Best Known (246−65, 246, s)-Nets in Base 3

(246−65, 246, 288)-Net over F₃ — Constructive and digital

Digital (181, 246, 288)-net over F₃, using

t-expansion [i] based on digital (177, 246, 288)-net over F₃, using
- 3 times m-reduction [i] based on digital (177, 249, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 83, 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]

(246−65, 246, 819)-Net over F₃ — Digital

Digital (181, 246, 819)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−65, 246, 28729)-Net in Base 3 — Upper bound on s

There is no (181, 246, 28730)-net in base 3, because

1 times m-reduction [i] would yield (181, 245, 28730)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 784 784071 016700 365684 132436 788646 042935 758628 950265 554428 622290 618984 852915 391881 020766 554593 889659 519342 178172 621633 > 3²⁴⁵ [i]