MinT - Best Known (176−73, 176, s)-Nets in Base 3

Best Known (176−73, 176, s)-Nets in Base 3

(176−73, 176, 128)-Net over F₃ — Constructive and digital

Digital (103, 176, 128)-net over F₃, using

4 times m-reduction [i] based on digital (103, 180, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 90, 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]

(176−73, 176, 151)-Net over F₃ — Digital

Digital (103, 176, 151)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−73, 176, 1454)-Net in Base 3 — Upper bound on s

There is no (103, 176, 1455)-net in base 3, because

1 times m-reduction [i] would yield (103, 175, 1455)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 318301 838832 629632 530359 890497 255572 565226 244525 207140 209226 101374 228897 657061 691321 > 3¹⁷⁵ [i]