Best Known (193, 193+35, s)-Nets in Base 3
(193, 193+35, 1496)-Net over F3 — Constructive and digital
Digital (193, 228, 1496)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (7, 24, 16)-net over F3, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 7 and N(F) ≥ 16, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
- 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
- trace code for nets [i] based on digital (16, 51, 370)-net over F81, using
- digital (7, 24, 16)-net over F3, using
(193, 193+35, 12567)-Net over F3 — Digital
Digital (193, 228, 12567)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3228, 12567, F3, 35) (dual of [12567, 12339, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(3228, 19748, F3, 35) (dual of [19748, 19520, 36]-code), using
- 5 times code embedding in larger space [i] based on linear OA(3223, 19743, F3, 35) (dual of [19743, 19520, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(27) [i] based on
- linear OA(3208, 19683, F3, 35) (dual of [19683, 19475, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(315, 60, F3, 6) (dual of [60, 45, 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
- 5 times code embedding in larger space [i] based on linear OA(3223, 19743, F3, 35) (dual of [19743, 19520, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(3228, 19748, F3, 35) (dual of [19748, 19520, 36]-code), using
(193, 193+35, large)-Net in Base 3 — Upper bound on s
There is no (193, 228, large)-net in base 3, because
- 33 times m-reduction [i] would yield (193, 195, large)-net in base 3, but