Best Known (202, 202+32, s)-Nets in Base 3
(202, 202+32, 11072)-Net over F3 — Constructive and digital
Digital (202, 234, 11072)-net over F3, using
- 32 times duplication [i] based on digital (200, 232, 11072)-net over F3, using
- net defined by OOA [i] based on linear OOA(3232, 11072, F3, 32, 32) (dual of [(11072, 32), 354072, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(3232, 177152, F3, 32) (dual of [177152, 176920, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3232, 177158, F3, 32) (dual of [177158, 176926, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(3232, 177147, F3, 32) (dual of [177147, 176915, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3221, 177147, F3, 31) (dual of [177147, 176926, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(30, 11, F3, 0) (dual of [11, 11, 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(31) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(3232, 177158, F3, 32) (dual of [177158, 176926, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(3232, 177152, F3, 32) (dual of [177152, 176920, 33]-code), using
- net defined by OOA [i] based on linear OOA(3232, 11072, F3, 32, 32) (dual of [(11072, 32), 354072, 33]-NRT-code), using
(202, 202+32, 48751)-Net over F3 — Digital
Digital (202, 234, 48751)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3234, 48751, F3, 3, 32) (dual of [(48751, 3), 146019, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3234, 59053, F3, 3, 32) (dual of [(59053, 3), 176925, 33]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3233, 59053, F3, 3, 32) (dual of [(59053, 3), 176926, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3233, 177159, F3, 32) (dual of [177159, 176926, 33]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3232, 177158, F3, 32) (dual of [177158, 176926, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(3232, 177147, F3, 32) (dual of [177147, 176915, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3221, 177147, F3, 31) (dual of [177147, 176926, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(30, 11, F3, 0) (dual of [11, 11, 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(31) ⊂ Ce(30) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3232, 177158, F3, 32) (dual of [177158, 176926, 33]-code), using
- OOA 3-folding [i] based on linear OA(3233, 177159, F3, 32) (dual of [177159, 176926, 33]-code), using
- 31 times duplication [i] based on linear OOA(3233, 59053, F3, 3, 32) (dual of [(59053, 3), 176926, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3234, 59053, F3, 3, 32) (dual of [(59053, 3), 176925, 33]-NRT-code), using
(202, 202+32, large)-Net in Base 3 — Upper bound on s
There is no (202, 234, large)-net in base 3, because
- 30 times m-reduction [i] would yield (202, 204, large)-net in base 3, but