MinT - Best Known (57−27, 57, s)-Nets in Base 5

Best Known (57−27, 57, s)-Nets in Base 5

(57−27, 57, 54)-Net over F₅ — Constructive and digital

Digital (30, 57, 54)-net over F₅, using

1 times m-reduction [i] based on digital (30, 58, 54)-net over F₅, using
- trace code for nets [i] based on digital (1, 29, 27)-net over F₂₅, using
  - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
    - Niederreiter sequence [i]

(57−27, 57, 83)-Net over F₅ — Digital

Digital (30, 57, 83)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(57−27, 57, 1443)-Net in Base 5 — Upper bound on s

There is no (30, 57, 1444)-net in base 5, because

1 times m-reduction [i] would yield (30, 56, 1444)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1389 441450 544601 765730 264227 789996 235537 > 5⁵⁶ [i]