MinT - Best Known (7, 12, s)-Nets in Base 4

Best Known (7, 12, s)-Nets in Base 4

(7, 12, 81)-Net over F₄ — Constructive and digital

Digital (7, 12, 81)-net over F₄, using

4¹ times duplication [i] based on digital (6, 11, 81)-net over F₄, using
- linear code embedding found in a computer search [i]

(7, 12, 96)-Net over F₄ — Digital

Digital (7, 12, 96)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4¹², 96, F₄, 5) (dual of [96, 84, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹², 106, F₄, 5) (dual of [106, 94, 6]-code), using
  - codes constructed by inverting constructionÂ Y₁ [i]

(7, 12, 964)-Net in Base 4 — Upper bound on s

There is no (7, 12, 965)-net in base 4, because

1 times m-reduction [i] would yield (7, 11, 965)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 4 200646 > 4¹¹ [i]