MinT - Best Known (205−86, 205, s)-Nets in Base 3

Best Known (205−86, 205, s)-Nets in Base 3

(205−86, 205, 128)-Net over F₃ — Constructive and digital

Digital (119, 205, 128)-net over F₃, using

7 times m-reduction [i] based on digital (119, 212, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 106, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(205−86, 205, 167)-Net over F₃ — Digital

Digital (119, 205, 167)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−86, 205, 1546)-Net in Base 3 — Upper bound on s

There is no (119, 205, 1547)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64 841414 063155 762554 164888 145934 070703 374436 236563 502213 790468 664624 757275 703299 127470 188248 126715 > 3²⁰⁵ [i]