MinT - Best Known (64−28, 64, s)-Nets in Base 25

Best Known (64−28, 64, s)-Nets in Base 25

(64−28, 64, 252)-Net over F₂₅ — Constructive and digital

Digital (36, 64, 252)-net over F₂₅, using

4 times m-reduction [i] based on digital (36, 68, 252)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 26, 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, 42, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(64−28, 64, 951)-Net over F₂₅ — Digital

Digital (36, 64, 951)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(64−28, 64, 619190)-Net in Base 25 — Upper bound on s

There is no (36, 64, 619191)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 293875 566122 194203 793598 424878 016518 611123 210197 075732 897501 608279 976853 758852 680249 807665 > 25⁶⁴ [i]