Best Known (169, 208, s)-Nets in Base 3
(169, 208, 896)-Net over F3 — Constructive and digital
Digital (169, 208, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 52, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
(169, 208, 3386)-Net over F3 — Digital
Digital (169, 208, 3386)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3208, 3386, F3, 39) (dual of [3386, 3178, 40]-code), using
- discarding factors / shortening the dual code based on linear OA(3208, 6560, F3, 39) (dual of [6560, 6352, 40]-code), using
- 1 times truncation [i] based on linear OA(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using
- an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- 1 times truncation [i] based on linear OA(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(3208, 6560, F3, 39) (dual of [6560, 6352, 40]-code), using
(169, 208, 625580)-Net in Base 3 — Upper bound on s
There is no (169, 208, 625581)-net in base 3, because
- 1 times m-reduction [i] would yield (169, 207, 625581)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 580 907200 115302 717246 425780 445914 141199 340765 531372 147227 319209 942918 237607 674759 805651 767997 795211 > 3207 [i]