Best Known (6, 6+11, s)-Nets in Base 3
(6, 6+11, 14)-Net over F3 — Constructive and digital
Digital (6, 17, 14)-net over F3, using
- net from sequence [i] based on digital (6, 13)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 6 and N(F) ≥ 14, using
(6, 6+11, 32)-Net over F3 — Upper bound on s (digital)
There is no digital (6, 17, 33)-net over F3, because
- 2 times m-reduction [i] would yield digital (6, 15, 33)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(315, 33, F3, 9) (dual of [33, 18, 10]-code), but
(6, 6+11, 39)-Net in Base 3 — Upper bound on s
There is no (6, 17, 40)-net in base 3, because
- 1 times m-reduction [i] would yield (6, 16, 40)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 45 576657 > 316 [i]