MinT - Best Known (53−25, 53, s)-Nets in Base 5

Best Known (53−25, 53, s)-Nets in Base 5

(53−25, 53, 54)-Net over F₅ — Constructive and digital

Digital (28, 53, 54)-net over F₅, using

1 times m-reduction [i] based on digital (28, 54, 54)-net over F₅, using
- trace code for nets [i] based on digital (1, 27, 27)-net over F₂₅, using
  - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
    - Niederreiter sequence [i]

(53−25, 53, 80)-Net over F₅ — Digital

Digital (28, 53, 80)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(53−25, 53, 1404)-Net in Base 5 — Upper bound on s

There is no (28, 53, 1405)-net in base 5, because

1 times m-reduction [i] would yield (28, 52, 1405)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 227735 029230 935637 366475 934538 187985 > 5⁵² [i]