Best Known (176, 200, s)-Nets in Base 3
(176, 200, 44290)-Net over F3 — Constructive and digital
Digital (176, 200, 44290)-net over F3, using
- 1 times m-reduction [i] based on digital (176, 201, 44290)-net over F3, using
- net defined by OOA [i] based on linear OOA(3201, 44290, F3, 25, 25) (dual of [(44290, 25), 1107049, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3201, 531481, F3, 25) (dual of [531481, 531280, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3201, 531482, F3, 25) (dual of [531482, 531281, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [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(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3201, 531482, F3, 25) (dual of [531482, 531281, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3201, 531481, F3, 25) (dual of [531481, 531280, 26]-code), using
- net defined by OOA [i] based on linear OOA(3201, 44290, F3, 25, 25) (dual of [(44290, 25), 1107049, 26]-NRT-code), using
(176, 200, 177161)-Net over F3 — Digital
Digital (176, 200, 177161)-net over F3, using
- 31 times duplication [i] based on digital (175, 199, 177161)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3199, 177161, F3, 3, 24) (dual of [(177161, 3), 531284, 25]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3199, 531483, F3, 24) (dual of [531483, 531284, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [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(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-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 Ce(24) ⊂ Ce(19) [i] based on
- OOA 3-folding [i] based on linear OA(3199, 531483, F3, 24) (dual of [531483, 531284, 25]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3199, 177161, F3, 3, 24) (dual of [(177161, 3), 531284, 25]-NRT-code), using
(176, 200, large)-Net in Base 3 — Upper bound on s
There is no (176, 200, large)-net in base 3, because
- 22 times m-reduction [i] would yield (176, 178, large)-net in base 3, but