MinT - Best Known (176−46, 176, s)-Nets in Base 3

Best Known (176−46, 176, s)-Nets in Base 3

(176−46, 176, 288)-Net over F₃ — Constructive and digital

Digital (130, 176, 288)-net over F₃, using

t-expansion [i] based on digital (129, 176, 288)-net over F₃, using
- 1 times m-reduction [i] based on digital (129, 177, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 59, 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]

(176−46, 176, 645)-Net over F₃ — Digital

Digital (130, 176, 645)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−46, 176, 21085)-Net in Base 3 — Upper bound on s

There is no (130, 176, 21086)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 941261 515623 421509 625755 220232 634057 286506 629035 119582 884154 147311 485569 822774 184473 > 3¹⁷⁶ [i]