MinT - Best Known (3, 3+5, s)-Nets in Base 4

Best Known (3, 3+5, s)-Nets in Base 4

(3, 3+5, 26)-Net over F₄ — Constructive and digital

Digital (3, 8, 26)-net over F₄, using

linear code embedding found in a computer search [i]

(3, 3+5, 59)-Net in Base 4 — Upper bound on s

There is no (3, 8, 60)-net in base 4, because

1 times m-reduction [i] would yield (3, 7, 60)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 16831 > 4⁷ [i]
- extracting embedded orthogonal array [i] would yield OA(4⁷, 60, S₄, 4), but
  - the linear programming bound shows that MÂ â‰¥ 14 400512 / 857 > 4⁷ [i]