MinT - Best Known (59, 59+48, s)-Nets in Base 25

Best Known (59, 59+48, s)-Nets in Base 25

(59, 59+48, 326)-Net over F₂₅ — Constructive and digital

Digital (59, 107, 326)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (10, 34, 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, 73, 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]

(59, 59+48, 1189)-Net over F₂₅ — Digital

Digital (59, 107, 1189)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+48, 697631)-Net in Base 25 — Upper bound on s

There is no (59, 107, 697632)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 379825 680013 514371 466734 668819 379800 329402 952164 035338 671968 001745 840980 578786 868255 749677 309192 045516 530157 264693 882981 894217 442912 442465 323845 146625 > 25¹⁰⁷ [i]