Best Known (168, 203, s)-Nets in Base 3
(168, 203, 896)-Net over F3 — Constructive and digital
Digital (168, 203, 896)-net over F3, using
- t-expansion [i] based on digital (166, 203, 896)-net over F3, using
- 1 times m-reduction [i] based on digital (166, 204, 896)-net over F3, using
- trace code for nets [i] based on digital (13, 51, 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, 51, 224)-net over F81, using
- 1 times m-reduction [i] based on digital (166, 204, 896)-net over F3, using
(168, 203, 5450)-Net over F3 — Digital
Digital (168, 203, 5450)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3203, 5450, F3, 35) (dual of [5450, 5247, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(3203, 6619, F3, 35) (dual of [6619, 6416, 36]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3200, 6616, F3, 35) (dual of [6616, 6416, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(27) [i] based on
- linear OA(3185, 6561, F3, 35) (dual of [6561, 6376, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3145, 6561, F3, 28) (dual of [6561, 6416, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(315, 55, F3, 6) (dual of [55, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- construction X applied to Ce(34) ⊂ Ce(27) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(3200, 6616, F3, 35) (dual of [6616, 6416, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(3203, 6619, F3, 35) (dual of [6619, 6416, 36]-code), using
(168, 203, 1675845)-Net in Base 3 — Upper bound on s
There is no (168, 203, 1675846)-net in base 3, because
- 1 times m-reduction [i] would yield (168, 202, 1675846)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 2 390528 484505 628718 157656 344969 349714 488585 059178 317385 496979 752958 981655 331389 274018 312692 026989 > 3202 [i]