MinT - Best Known (5, 12, s)-Nets in Base 5

Best Known (5, 12, s)-Nets in Base 5

(5, 12, 25)-Net over F₅ — Constructive and digital

Digital (5, 12, 25)-net over F₅, using

5² times duplication [i] based on digital (3, 10, 25)-net over F₅, using
- linear code embedding found in a computer search [i]

(5, 12, 26)-Net over F₅ — Digital

Digital (5, 12, 26)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(5¹², 26, F₅, 2, 7) (dual of [(26, 2), 40, 8]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(5¹⁰, 25, F₅, 2, 7) (dual of [(25, 2), 40, 8]-NRT-code), using
  - extracting embedded OOA [i] based on digital (3, 10, 25)-net over F₅, using
    - linear code embedding found in a computer search [i]

(5, 12, 164)-Net in Base 5 — Upper bound on s

There is no (5, 12, 165)-net in base 5, because

1 times m-reduction [i] would yield (5, 11, 165)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 49 450061 > 5¹¹ [i]