MinT - Best Known (36, 36+25, s)-Nets in Base 25

Best Known (36, 36+25, s)-Nets in Base 25

(36, 36+25, 252)-Net over F₂₅ — Constructive and digital

Digital (36, 61, 252)-net over F₂₅, using

7 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)

(36, 36+25, 1472)-Net over F₂₅ — Digital

Digital (36, 61, 1472)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(36, 36+25, 2152033)-Net in Base 25 — Upper bound on s

There is no (36, 61, 2152034)-net in base 25, because

1 times m-reduction [i] would yield (36, 60, 2152034)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 752318 961830 084637 640185 187020 278604 441679 179132 428892 209862 428987 121741 316075 844545 > 25⁶⁰ [i]