Best Known (104−11, 104, s)-Nets in Base 3
(104−11, 104, 956600)-Net over F3 — Constructive and digital
Digital (93, 104, 956600)-net over F3, using
- 31 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(3103, 956600, F3, 11, 11) (dual of [(956600, 11), 10522497, 12]-NRT-code), using
(104−11, 104, 2280104)-Net over F3 — Digital
Digital (93, 104, 2280104)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3104, 2280104, F3, 2, 11) (dual of [(2280104, 2), 4560104, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3104, 2391501, F3, 2, 11) (dual of [(2391501, 2), 4782898, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3104, 4783002, F3, 11) (dual of [4783002, 4782898, 12]-code), using
- 1 times code embedding in larger space [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
- 1 times code embedding in larger space [i] based on linear OA(3103, 4783001, F3, 11) (dual of [4783001, 4782898, 12]-code), using
- OOA 2-folding [i] based on linear OA(3104, 4783002, F3, 11) (dual of [4783002, 4782898, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(3104, 2391501, F3, 2, 11) (dual of [(2391501, 2), 4782898, 12]-NRT-code), using
(104−11, 104, large)-Net in Base 3 — Upper bound on s
There is no (93, 104, large)-net in base 3, because
- 9 times m-reduction [i] would yield (93, 95, large)-net in base 3, but