MinT - Best Known (93−25, 93, s)-Nets in Base 5

Best Known (93−25, 93, s)-Nets in Base 5

(93−25, 93, 296)-Net over F₅ — Constructive and digital

Digital (68, 93, 296)-net over F₅, using

5 times m-reduction [i] based on digital (68, 98, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 49, 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]

(93−25, 93, 1264)-Net over F₅ — Digital

Digital (68, 93, 1264)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−25, 93, 302036)-Net in Base 5 — Upper bound on s

There is no (68, 93, 302037)-net in base 5, because

1 times m-reduction [i] would yield (68, 92, 302037)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 20195 349250 562359 952255 514271 414149 898542 988830 584161 673110 925265 > 5⁹² [i]