Best Known (200−25, 200, s)-Nets in Base 3
(200−25, 200, 44289)-Net over F3 — Constructive and digital
Digital (175, 200, 44289)-net over F3, using
- 33 times duplication [i] based on digital (172, 197, 44289)-net over F3, using
- net defined by OOA [i] based on linear OOA(3197, 44289, F3, 25, 25) (dual of [(44289, 25), 1107028, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3197, 531469, F3, 25) (dual of [531469, 531272, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(3193, 531441, F3, 25) (dual of [531441, 531248, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(34, 28, F3, 2) (dual of [28, 24, 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(24) ⊂ Ce(21) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(3197, 531469, F3, 25) (dual of [531469, 531272, 26]-code), using
- net defined by OOA [i] based on linear OOA(3197, 44289, F3, 25, 25) (dual of [(44289, 25), 1107028, 26]-NRT-code), using
(200−25, 200, 132868)-Net over F3 — Digital
Digital (175, 200, 132868)-net over F3, using
- 31 times duplication [i] based on digital (174, 199, 132868)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3199, 132868, F3, 4, 25) (dual of [(132868, 4), 531273, 26]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3199, 531472, F3, 25) (dual of [531472, 531273, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(3193, 531442, F3, 25) (dual of [531442, 531249, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3169, 531442, F3, 21) (dual of [531442, 531273, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(36, 30, F3, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- OOA 4-folding [i] based on linear OA(3199, 531472, F3, 25) (dual of [531472, 531273, 26]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3199, 132868, F3, 4, 25) (dual of [(132868, 4), 531273, 26]-NRT-code), using
(200−25, 200, large)-Net in Base 3 — Upper bound on s
There is no (175, 200, large)-net in base 3, because
- 23 times m-reduction [i] would yield (175, 177, large)-net in base 3, but