MinT - Best Known (115−25, 115, s)-Nets in Base 5

Best Known (115−25, 115, s)-Nets in Base 5

(115−25, 115, 504)-Net over F₅ — Constructive and digital

Digital (90, 115, 504)-net over F₅, using

5¹ times duplication [i] based on digital (89, 114, 504)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (32, 44, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 22, 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 (45, 70, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 35, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(115−25, 115, 5489)-Net over F₅ — Digital

Digital (90, 115, 5489)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−25, 115, 5774519)-Net in Base 5 — Upper bound on s

There is no (90, 115, 5774520)-net in base 5, because

1 times m-reduction [i] would yield (90, 114, 5774520)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 148335 877882 489772 439509 928533 088339 202976 524532 105048 456472 471531 997231 629313 > 5¹¹⁴ [i]