MinT - Best Known (49−23, 49, s)-Nets in Base 5

Best Known (49−23, 49, s)-Nets in Base 5

(49−23, 49, 54)-Net over F₅ — Constructive and digital

Digital (26, 49, 54)-net over F₅, using

1 times m-reduction [i] based on digital (26, 50, 54)-net over F₅, using
- trace code for nets [i] based on digital (1, 25, 27)-net over F₂₅, using
  - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
    - Niederreiter sequence [i]

(49−23, 49, 76)-Net over F₅ — Digital

Digital (26, 49, 76)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(49−23, 49, 1369)-Net in Base 5 — Upper bound on s

There is no (26, 49, 1370)-net in base 5, because

1 times m-reduction [i] would yield (26, 48, 1370)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3567 164218 326437 871070 187890 582793 > 5⁴⁸ [i]