MinT - Best Known (121−41, 121, s)-Nets in Base 5

Best Known (121−41, 121, s)-Nets in Base 5

(121−41, 121, 296)-Net over F₅ — Constructive and digital

Digital (80, 121, 296)-net over F₅, using

1 times m-reduction [i] based on digital (80, 122, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 61, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(121−41, 121, 520)-Net over F₅ — Digital

Digital (80, 121, 520)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−41, 121, 32424)-Net in Base 5 — Upper bound on s

There is no (80, 121, 32425)-net in base 5, because

1 times m-reduction [i] would yield (80, 120, 32425)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 752588 566331 610821 954943 738337 043854 662106 935811 096134 262165 371132 422020 043296 926001 > 5¹²⁰ [i]