MinT - Best Known (62, 62+39, s)-Nets in Base 25

Best Known (62, 62+39, s)-Nets in Base 25

(62, 62+39, 378)-Net over F₂₅ — Constructive and digital

Digital (62, 101, 378)-net over F₂₅, using

generalized (u,Â u+v)-construction [i] based on
1. digital (10, 23, 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, 29, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)
3. digital (10, 49, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(62, 62+39, 3271)-Net over F₂₅ — Digital

Digital (62, 101, 3271)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+39, 7526320)-Net in Base 25 — Upper bound on s

There is no (62, 101, 7526321)-net in base 25, because

1 times m-reduction [i] would yield (62, 100, 7526321)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 62 230273 960265 532039 244844 534652 635608 013577 132079 329401 098859 227891 450081 178172 116147 955244 751050 170765 807732 324419 798077 990881 021889 540105 > 25¹⁰⁰ [i]