MinT - Best Known (147−47, 147, s)-Nets in Base 5

Best Known (147−47, 147, s)-Nets in Base 5

(147−47, 147, 400)-Net over F₅ — Constructive and digital

Digital (100, 147, 400)-net over F₅, using

3 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]

(147−47, 147, 787)-Net over F₅ — Digital

Digital (100, 147, 787)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−47, 147, 64450)-Net in Base 5 — Upper bound on s

There is no (100, 147, 64451)-net in base 5, because

1 times m-reduction [i] would yield (100, 146, 64451)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 121406 141644 083098 458645 609843 163522 346893 469598 945422 639789 720790 440408 676572 991042 637100 244885 156725 > 5¹⁴⁶ [i]