MinT - Best Known (113−36, 113, s)-Nets in Base 3

Best Known (113−36, 113, s)-Nets in Base 3

(113−36, 113, 148)-Net over F₃ — Constructive and digital

Digital (77, 113, 148)-net over F₃, using

7 times m-reduction [i] based on digital (77, 120, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 60, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(113−36, 113, 228)-Net over F₃ — Digital

Digital (77, 113, 228)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−36, 113, 3718)-Net in Base 3 — Upper bound on s

There is no (77, 113, 3719)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 825081 891326 112694 197456 108071 335585 213579 232171 848045 > 3¹¹³ [i]