MinT - Best Known (103, 103+45, s)-Nets in Base 5

Best Known (103, 103+45, s)-Nets in Base 5

(103, 103+45, 400)-Net over F₅ — Constructive and digital

Digital (103, 148, 400)-net over F₅, using

t-expansion [i] based on digital (100, 148, 400)-net over F₅, using
- 2 times m-reduction [i] based on digital (100, 150, 400)-net over F₅, using
  - trace code for nets [i] based on digital (25, 75, 200)-net over F₂₅, using
    - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
        a function field by GarcÃa and Quoos [i]

(103, 103+45, 990)-Net over F₅ — Digital

Digital (103, 148, 990)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+45, 105954)-Net in Base 5 — Upper bound on s

There is no (103, 148, 105955)-net in base 5, because

1 times m-reduction [i] would yield (103, 147, 105955)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 606190 553961 429231 916689 742876 060789 701641 093897 205163 582157 491087 874833 264659 452001 161285 814778 589865 > 5¹⁴⁷ [i]