MinT - Best Known (97, 97+53, s)-Nets in Base 5

Best Known (97, 97+53, s)-Nets in Base 5

(97, 97+53, 296)-Net over F₅ — Constructive and digital

Digital (97, 150, 296)-net over F₅, using

t-expansion [i] based on digital (94, 150, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 75, 148)-net over F₂₅, using
  - net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
      - a function field by GarcÃa and Quoos [i]

(97, 97+53, 516)-Net over F₅ — Digital

Digital (97, 150, 516)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 97+53, 26702)-Net in Base 5 — Upper bound on s

There is no (97, 150, 26703)-net in base 5, because

1 times m-reduction [i] would yield (97, 149, 26703)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 130169 975866 190064 212926 769600 811096 354297 123567 907568 265123 558236 268033 756873 420734 018737 269639 250841 > 5¹⁴⁹ [i]