MinT - Best Known (58, 58+46, s)-Nets in Base 25

Best Known (58, 58+46, s)-Nets in Base 25

(58, 58+46, 326)-Net over F₂₅ — Constructive and digital

Digital (58, 104, 326)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (10, 33, 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]
2. digital (25, 71, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(58, 58+46, 1272)-Net over F₂₅ — Digital

Digital (58, 104, 1272)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+46, 822922)-Net in Base 25 — Upper bound on s

There is no (58, 104, 822923)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 24 309212 870301 352352 381756 463726 239057 927727 853149 916995 783746 264745 109526 929091 005491 435838 373789 490347 432581 473867 914652 748423 300916 970301 332025 > 25¹⁰⁴ [i]