MinT - Best Known (97, 148, s)-Nets in Base 5

Best Known (97, 148, s)-Nets in Base 5

(97, 148, 296)-Net over F₅ — Constructive and digital

Digital (97, 148, 296)-net over F₅, using

t-expansion [i] based on digital (94, 148, 296)-net over F₅, using
- 2 times m-reduction [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, 148, 567)-Net over F₅ — Digital

Digital (97, 148, 567)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(97, 148, 32754)-Net in Base 5 — Upper bound on s

There is no (97, 148, 32755)-net in base 5, because

1 times m-reduction [i] would yield (97, 147, 32755)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 608421 763681 054874 217229 633235 538642 783145 389202 087244 758085 443107 624167 562544 560149 657428 826875 315565 > 5¹⁴⁷ [i]