MinT - Best Known (4, 4+5, s)-Nets in Base 4

Best Known (4, 4+5, s)-Nets in Base 4

(4, 4+5, 36)-Net over F₄ — Constructive and digital

Digital (4, 9, 36)-net over F₄, using

linear code embedding found in a computer search [i]

(4, 4+5, 119)-Net in Base 4 — Upper bound on s

There is no (4, 9, 120)-net in base 4, because

1 times m-reduction [i] would yield (4, 8, 120)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 66061 > 4⁸ [i]
- extracting embedded orthogonal array [i] would yield OA(4⁸, 120, S₄, 4), but
  - the linear programming bound shows that MÂ â‰¥ 12 287680 / 187 > 4⁸ [i]