Best Known (6−5, 6, s)-Nets in Base 5
(6−5, 6, 10)-Net over F5 — Constructive and digital
Digital (1, 6, 10)-net over F5, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 1 and N(F) ≥ 10, using
(6−5, 6, 12)-Net over F5 — Upper bound on s (digital)
There is no digital (1, 6, 13)-net over F5, because
- 1 times m-reduction [i] would yield digital (1, 5, 13)-net over F5, but
- extracting embedded orthogonal array [i] would yield linear OA(55, 13, F5, 4) (dual of [13, 8, 5]-code), but
- “Bou†bound on codes from Brouwer’s database [i]
- extracting embedded orthogonal array [i] would yield linear OA(55, 13, F5, 4) (dual of [13, 8, 5]-code), but
(6−5, 6, 17)-Net in Base 5 — Upper bound on s
There is no (1, 6, 18)-net in base 5, because
- extracting embedded OOA [i] would yield OOA(56, 18, S5, 2, 5), but
- the linear programming bound for OOAs shows that M ≥ 61 625000 / 3807 > 56 [i]