Best Known (2, 14, s)-Nets in Base 9
(2, 14, 20)-Net over F9 — Constructive and digital
Digital (2, 14, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
(2, 14, 43)-Net over F9 — Upper bound on s (digital)
There is no digital (2, 14, 44)-net over F9, because
- extracting embedded orthogonal array [i] would yield linear OA(914, 44, F9, 12) (dual of [44, 30, 13]-code), but
- construction Y1 [i] would yield
- linear OA(913, 17, F9, 12) (dual of [17, 4, 13]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- linear OA(930, 44, F9, 27) (dual of [44, 14, 28]-code), but
- discarding factors / shortening the dual code would yield linear OA(930, 39, F9, 27) (dual of [39, 9, 28]-code), but
- residual code [i] would yield OA(93, 11, S9, 3), but
- discarding factors / shortening the dual code would yield linear OA(930, 39, F9, 27) (dual of [39, 9, 28]-code), but
- linear OA(913, 17, F9, 12) (dual of [17, 4, 13]-code), but
- construction Y1 [i] would yield
(2, 14, 59)-Net in Base 9 — Upper bound on s
There is no (2, 14, 60)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 23 188827 548097 > 914 [i]