MinT - Best Known (180, 180+66, s)-Nets in Base 3

Best Known (180, 180+66, s)-Nets in Base 3

(180, 180+66, 288)-Net over F₃ — Constructive and digital

Digital (180, 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]

(180, 180+66, 775)-Net over F₃ — Digital

Digital (180, 246, 775)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+66, 23683)-Net in Base 3 — Upper bound on s

There is no (180, 246, 23684)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2354 846801 140838 632384 622591 762139 471290 808759 914288 240238 151564 782615 064741 469394 034426 302274 309981 248929 290687 040265 > 3²⁴⁶ [i]