Best Known (169, 204, s)-Nets in Base 3
(169, 204, 1480)-Net over F3 — Constructive and digital
Digital (169, 204, 1480)-net over F3, using
- trace code for nets [i] based on digital (16, 51, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(169, 204, 5635)-Net over F3 — Digital
Digital (169, 204, 5635)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3204, 5635, F3, 35) (dual of [5635, 5431, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(3204, 6620, F3, 35) (dual of [6620, 6416, 36]-code), using
- 4 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
- 4 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(3204, 6620, F3, 35) (dual of [6620, 6416, 36]-code), using
(169, 204, 1787723)-Net in Base 3 — Upper bound on s
There is no (169, 204, 1787724)-net in base 3, because
- 1 times m-reduction [i] would yield (169, 203, 1787724)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 7 171624 661979 861722 764476 081930 899853 788435 407370 308813 343658 235805 079736 409342 818175 387942 646937 > 3203 [i]