Best Known (14−11, 14, s)-Nets in Base 4
(14−11, 14, 14)-Net over F4 — Constructive and digital
Digital (3, 14, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
(14−11, 14, 17)-Net over F4 — Upper bound on s (digital)
There is no digital (3, 14, 18)-net over F4, because
- 1 times m-reduction [i] would yield digital (3, 13, 18)-net over F4, but
- extracting embedded orthogonal array [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- “Liz†bound on codes from Brouwer’s database [i]
- extracting embedded orthogonal array [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
(14−11, 14, 26)-Net in Base 4 — Upper bound on s
There is no (3, 14, 27)-net in base 4, because
- extracting embedded OOA [i] would yield OOA(414, 27, S4, 2, 11), but
- the linear programming bound for OOAs shows that M ≥ 155139 175869 634215 235168 629529 972923 624018 935808 / 568 151163 776606 465868 481968 204197 426287 > 414 [i]