MinT - Best Known (93, 93+53, s)-Nets in Base 5

Best Known (93, 93+53, s)-Nets in Base 5

(93, 93+53, 296)-Net over F₅ — Constructive and digital

Digital (93, 146, 296)-net over F₅, using

2 times m-reduction [i] based on digital (93, 148, 296)-net over F₅, using
- trace code for nets [i] based on digital (19, 74, 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, 93+53, 452)-Net over F₅ — Digital

Digital (93, 146, 452)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+53, 20842)-Net in Base 5 — Upper bound on s

There is no (93, 146, 20843)-net in base 5, because

1 times m-reduction [i] would yield (93, 145, 20843)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 224487 339157 661442 802485 488170 169528 727351 882212 268590 531588 765118 115934 694775 737705 684160 880480 125721 > 5¹⁴⁵ [i]