Best Known (5, 16, s)-Nets in Base 3
(5, 16, 13)-Net over F3 — Constructive and digital
Digital (5, 16, 13)-net over F3, using
- net from sequence [i] based on digital (5, 12)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 4, N(F) = 12, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 4 and N(F) ≥ 12, using an explicitly constructive algebraic function field [i]
(5, 16, 23)-Net over F3 — Upper bound on s (digital)
There is no digital (5, 16, 24)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(316, 24, F3, 11) (dual of [24, 8, 12]-code), but
(5, 16, 30)-Net in Base 3 — Upper bound on s
There is no (5, 16, 31)-net in base 3, because
- 1 times m-reduction [i] would yield (5, 15, 31)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 14 554935 > 315 [i]