Best Known (223−40, 223, s)-Nets in Base 3
(223−40, 223, 896)-Net over F3 — Constructive and digital
Digital (183, 223, 896)-net over F3, using
- t-expansion [i] based on digital (181, 223, 896)-net over F3, using
- 1 times m-reduction [i] based on digital (181, 224, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 56, 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
- trace code for nets [i] based on digital (13, 56, 224)-net over F81, using
- 1 times m-reduction [i] based on digital (181, 224, 896)-net over F3, using
(223−40, 223, 4568)-Net over F3 — Digital
Digital (183, 223, 4568)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3223, 4568, F3, 40) (dual of [4568, 4345, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(3223, 6607, F3, 40) (dual of [6607, 6384, 41]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3220, 6604, F3, 40) (dual of [6604, 6384, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(33) [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]
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(311, 43, F3, 5) (dual of [43, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(39) ⊂ Ce(33) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(3220, 6604, F3, 40) (dual of [6604, 6384, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(3223, 6607, F3, 40) (dual of [6607, 6384, 41]-code), using
(223−40, 223, 867298)-Net in Base 3 — Upper bound on s
There is no (183, 223, 867299)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 25006 188195 632888 943442 866763 715610 809617 672595 579413 597895 540914 537016 391127 011893 277918 272398 459179 629241 > 3223 [i]