Best Known (181, 181+22, s)-Nets in Base 3
(181, 181+22, 434818)-Net over F3 — Constructive and digital
Digital (181, 203, 434818)-net over F3, using
- 32 times duplication [i] based on digital (179, 201, 434818)-net over F3, using
- net defined by OOA [i] based on linear OOA(3201, 434818, F3, 22, 22) (dual of [(434818, 22), 9565795, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3201, 4782998, F3, 22) (dual of [4782998, 4782797, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3201, 4783001, F3, 22) (dual of [4783001, 4782800, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3169, 4782969, F3, 19) (dual of [4782969, 4782800, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3201, 4783001, F3, 22) (dual of [4783001, 4782800, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3201, 4782998, F3, 22) (dual of [4782998, 4782797, 23]-code), using
- net defined by OOA [i] based on linear OOA(3201, 434818, F3, 22, 22) (dual of [(434818, 22), 9565795, 23]-NRT-code), using
(181, 181+22, 1195750)-Net over F3 — Digital
Digital (181, 203, 1195750)-net over F3, using
- 32 times duplication [i] based on digital (179, 201, 1195750)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3201, 1195750, F3, 4, 22) (dual of [(1195750, 4), 4782799, 23]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3201, 4783000, F3, 22) (dual of [4783000, 4782799, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3201, 4783001, F3, 22) (dual of [4783001, 4782800, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3169, 4782969, F3, 19) (dual of [4782969, 4782800, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(21) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(3201, 4783001, F3, 22) (dual of [4783001, 4782800, 23]-code), using
- OOA 4-folding [i] based on linear OA(3201, 4783000, F3, 22) (dual of [4783000, 4782799, 23]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3201, 1195750, F3, 4, 22) (dual of [(1195750, 4), 4782799, 23]-NRT-code), using
(181, 181+22, large)-Net in Base 3 — Upper bound on s
There is no (181, 203, large)-net in base 3, because
- 20 times m-reduction [i] would yield (181, 183, large)-net in base 3, but