MinT - Best Known (60, 60+43, s)-Nets in Base 25

Best Known (60, 60+43, s)-Nets in Base 25

(60, 60+43, 326)-Net over F₂₅ — Constructive and digital

Digital (60, 103, 326)-net over F₂₅, using

7 times m-reduction [i] based on digital (60, 110, 326)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 35, 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, 75, 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]

(60, 60+43, 1865)-Net over F₂₅ — Digital

Digital (60, 103, 1865)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+43, 2229839)-Net in Base 25 — Upper bound on s

There is no (60, 103, 2229840)-net in base 25, because

1 times m-reduction [i] would yield (60, 102, 2229840)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 38894 158630 777444 936682 299346 210530 430938 582066 497200 059056 248351 046153 361552 642851 798137 100334 564622 147147 148718 005933 171733 240358 350057 144705 > 25¹⁰² [i]