MinT - Best Known (11−5, 11, s)-Nets in Base 5

Best Known (11−5, 11, s)-Nets in Base 5

(11−5, 11, 68)-Net over F₅ — Constructive and digital

Digital (6, 11, 68)-net over F₅, using

5¹ times duplication [i] based on digital (5, 10, 68)-net over F₅, using
- linear code embedding found in a computer search [i]

(11−5, 11, 96)-Net over F₅ — Digital

Digital (6, 11, 96)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5¹¹, 96, F₅, 5) (dual of [96, 85, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹¹, 102, F₅, 5) (dual of [102, 91, 6]-code), using
  - codes constructed by inverting constructionÂ Y₁ [i]

(11−5, 11, 1103)-Net in Base 5 — Upper bound on s

There is no (6, 11, 1104)-net in base 5, because

1 times m-reduction [i] would yield (6, 10, 1104)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9 768193 > 5¹⁰ [i]