MinT - Best Known (121−45, 121, s)-Nets in Base 5

Best Known (121−45, 121, s)-Nets in Base 5

(121−45, 121, 252)-Net over F₅ — Constructive and digital

Digital (76, 121, 252)-net over F₅, using

11 times m-reduction [i] based on digital (76, 132, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 66, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(121−45, 121, 352)-Net over F₅ — Digital

Digital (76, 121, 352)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−45, 121, 14685)-Net in Base 5 — Upper bound on s

There is no (76, 121, 14686)-net in base 5, because

1 times m-reduction [i] would yield (76, 120, 14686)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 753061 324026 241183 419063 803882 265434 851237 312353 665719 901302 202221 807112 693371 148225 > 5¹²⁰ [i]