MinT - Best Known (93, 138, s)-Nets in Base 5

Best Known (93, 138, s)-Nets in Base 5

(93, 138, 296)-Net over F₅ — Constructive and digital

Digital (93, 138, 296)-net over F₅, using

10 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, 138, 684)-Net over F₅ — Digital

Digital (93, 138, 684)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 138, 50972)-Net in Base 5 — Upper bound on s

There is no (93, 138, 50973)-net in base 5, because

1 times m-reduction [i] would yield (93, 137, 50973)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 574163 736596 495178 052349 496474 860060 849725 531525 769715 259637 417186 385891 962677 542544 321015 662921 > 5¹³⁷ [i]