Best Known (92, 92+11, s)-Nets in Base 3
(92, 92+11, 956600)-Net over F3 — Constructive and digital
Digital (92, 103, 956600)-net over F3, using
- net defined by OOA [i] based on linear OOA(3103, 956600, F3, 11, 11) (dual of [(956600, 11), 10522497, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3103, 4783001, F3, 11) (dual of [4783001, 4782898, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(371, 4782969, F3, 8) (dual of [4782969, 4782898, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(34, 32, F3, 2) (dual of [32, 28, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- OOA 5-folding and stacking with additional row [i] based on linear OA(3103, 4783001, F3, 11) (dual of [4783001, 4782898, 12]-code), using
(92, 92+11, 1987533)-Net over F3 — Digital
Digital (92, 103, 1987533)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3103, 1987533, F3, 2, 11) (dual of [(1987533, 2), 3974963, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3103, 2391500, F3, 2, 11) (dual of [(2391500, 2), 4782897, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3103, 4783000, F3, 11) (dual of [4783000, 4782897, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(3103, 4783001, F3, 11) (dual of [4783001, 4782898, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(399, 4782969, F3, 11) (dual of [4782969, 4782870, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(371, 4782969, F3, 8) (dual of [4782969, 4782898, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(34, 32, F3, 2) (dual of [32, 28, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(3103, 4783001, F3, 11) (dual of [4783001, 4782898, 12]-code), using
- OOA 2-folding [i] based on linear OA(3103, 4783000, F3, 11) (dual of [4783000, 4782897, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(3103, 2391500, F3, 2, 11) (dual of [(2391500, 2), 4782897, 12]-NRT-code), using
(92, 92+11, large)-Net in Base 3 — Upper bound on s
There is no (92, 103, large)-net in base 3, because
- 9 times m-reduction [i] would yield (92, 94, large)-net in base 3, but