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

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

(12−7, 12, 20)-Net over F₄ — Constructive and digital

Digital (5, 12, 20)-net over F₄, using

4¹ times duplication [i] based on digital (4, 11, 20)-net over F₄, using
- linear code embedding found in a computer search [i]

(12−7, 12, 95)-Net in Base 4 — Upper bound on s

There is no (5, 12, 96)-net in base 4, because

1 times m-reduction [i] would yield (5, 11, 96)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 4 233169 > 4¹¹ [i]