MinT - Best Known (10−5, 10, s)-Nets in Base 4

Best Known (10−5, 10, s)-Nets in Base 4

(10−5, 10, 64)-Net over F₄ — Constructive and digital

Digital (5, 10, 64)-net over F₄, using

linear code embedding found in a computer search [i]

(10−5, 10, 240)-Net in Base 4 — Upper bound on s

There is no (5, 10, 241)-net in base 4, because

1 times m-reduction [i] would yield (5, 9, 241)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 263896 > 4⁹ [i]
- extracting embedded orthogonal array [i] would yield OA(4⁹, 241, S₄, 4), but
  - the linear programming bound shows that MÂ â‰¥ 2854 667200 / 10873 > 4⁹ [i]