MinT - Best Known (121−37, 121, s)-Nets in Base 5

Best Known (121−37, 121, s)-Nets in Base 5

(121−37, 121, 296)-Net over F₅ — Constructive and digital

Digital (84, 121, 296)-net over F₅, using

9 times m-reduction [i] based on digital (84, 130, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 65, 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]

(121−37, 121, 816)-Net over F₅ — Digital

Digital (84, 121, 816)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−37, 121, 86259)-Net in Base 5 — Upper bound on s

There is no (84, 121, 86260)-net in base 5, because

1 times m-reduction [i] would yield (84, 120, 86260)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 752466 140532 913450 985033 916221 928821 611124 745754 358214 164111 803824 962405 730127 986625 > 5¹²⁰ [i]