Best Known (183−10, 183, s)-Nets in Base 3
(183−10, 183, 7424655)-Net over F3 — Constructive and digital
Digital (173, 183, 7424655)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (40, 45, 2391495)-net over F3, using
- net defined by OOA [i] based on linear OOA(345, 2391495, F3, 5, 5) (dual of [(2391495, 5), 11957430, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(345, 2391495, F3, 4, 5) (dual of [(2391495, 4), 9565935, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(32, 4, F3, 4, 2) (dual of [(4, 4), 14, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;14,3) [i]
- linear OOA(343, 2391491, F3, 4, 5) (dual of [(2391491, 4), 9565921, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(329, 4782969, F3, 4) (dual of [4782969, 4782940, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- linear OOA(32, 4, F3, 4, 2) (dual of [(4, 4), 14, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(345, 2391495, F3, 4, 5) (dual of [(2391495, 4), 9565935, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(345, 2391495, F3, 5, 5) (dual of [(2391495, 5), 11957430, 6]-NRT-code), using
- digital (128, 138, 5033160)-net over F3, using
- trace code for nets [i] based on digital (36, 46, 1677720)-net over F27, using
- net defined by OOA [i] based on linear OOA(2746, 1677720, F27, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2746, 8388600, F27, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2746, large, F27, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2746, large, F27, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2746, 8388600, F27, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(2746, 1677720, F27, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- trace code for nets [i] based on digital (36, 46, 1677720)-net over F27, using
- digital (40, 45, 2391495)-net over F3, using
(183−10, 183, large)-Net over F3 — Digital
Digital (173, 183, large)-net over F3, using
- 35 times duplication [i] based on digital (168, 178, large)-net over F3, using
- t-expansion [i] based on digital (163, 178, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3178, large, F3, 15) (dual of [large, large−178, 16]-code), using
- 28 times code embedding in larger space [i] based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- 28 times code embedding in larger space [i] based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3178, large, F3, 15) (dual of [large, large−178, 16]-code), using
- t-expansion [i] based on digital (163, 178, large)-net over F3, using
(183−10, 183, large)-Net in Base 3 — Upper bound on s
There is no (173, 183, large)-net in base 3, because
- 8 times m-reduction [i] would yield (173, 175, large)-net in base 3, but