MinT - Best Known (121−42, 121, s)-Nets in Base 9

Best Known (121−42, 121, s)-Nets in Base 9

(121−42, 121, 740)-Net over F₉ — Constructive and digital

Digital (79, 121, 740)-net over F₉, using

5 times m-reduction [i] based on digital (79, 126, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 63, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(121−42, 121, 1342)-Net over F₉ — Digital

Digital (79, 121, 1342)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−42, 121, 341696)-Net in Base 9 — Upper bound on s

There is no (79, 121, 341697)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29 063456 259710 560029 171379 213957 570303 933046 343051 096570 931791 265501 017266 179188 388943 804545 103918 820813 190644 180777 > 9¹²¹ [i]