MinT - Best Known (95, 95+49, s)-Nets in Base 3

Best Known (95, 95+49, s)-Nets in Base 3

(95, 95+49, 156)-Net over F₃ — Constructive and digital

Digital (95, 144, 156)-net over F₃, using

2 times m-reduction [i] based on digital (95, 146, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 73, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(95, 95+49, 227)-Net over F₃ — Digital

Digital (95, 144, 227)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(95, 95+49, 3389)-Net in Base 3 — Upper bound on s

There is no (95, 144, 3390)-net in base 3, because

1 times m-reduction [i] would yield (95, 143, 3390)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 169 280207 640188 729689 075940 771286 933542 831208 989396 084909 665859 702769 > 3¹⁴³ [i]