MinT - Best Known (103, 103+47, s)-Nets in Base 5

Best Known (103, 103+47, s)-Nets in Base 5

(103, 103+47, 400)-Net over F₅ — Constructive and digital

Digital (103, 150, 400)-net over F₅, using

t-expansion [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+47, 879)-Net over F₅ — Digital

Digital (103, 150, 879)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 103+47, 79508)-Net in Base 5 — Upper bound on s

There is no (103, 150, 79509)-net in base 5, because

1 times m-reduction [i] would yield (103, 149, 79509)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 140610 486834 648428 771033 678761 577052 128819 894243 494484 180808 192374 636148 652823 738935 530228 146857 484925 > 5¹⁴⁹ [i]