MinT - Best Known (65, 105, s)-Nets in Base 25

Best Known (65, 105, s)-Nets in Base 25

(65, 105, 378)-Net over F₂₅ — Constructive and digital

Digital (65, 105, 378)-net over F₂₅, using

3 times m-reduction [i] based on digital (65, 108, 378)-net over F₂₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (10, 24, 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 (10, 31, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)
  3. digital (10, 53, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(65, 105, 3743)-Net over F₂₅ — Digital

Digital (65, 105, 3743)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 105, 7555782)-Net in Base 25 — Upper bound on s

There is no (65, 105, 7555783)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 607 717340 272283 508220 171436 708209 976495 467101 625659 198311 876153 279803 252365 697304 225723 426356 516507 946680 335473 677469 804539 045686 666118 271894 693665 > 25¹⁰⁵ [i]