Best Known (205−22, 205, s)-Nets in Base 3
(205−22, 205, 434819)-Net over F3 — Constructive and digital
Digital (183, 205, 434819)-net over F3, using
- net defined by OOA [i] based on linear OOA(3205, 434819, F3, 22, 22) (dual of [(434819, 22), 9565813, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3205, 4783009, F3, 22) (dual of [4783009, 4782804, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3205, 4783010, F3, 22) (dual of [4783010, 4782805, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [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(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3205, 4783010, F3, 22) (dual of [4783010, 4782805, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3205, 4783009, F3, 22) (dual of [4783009, 4782804, 23]-code), using
(205−22, 205, 1195752)-Net over F3 — Digital
Digital (183, 205, 1195752)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3205, 1195752, F3, 4, 22) (dual of [(1195752, 4), 4782803, 23]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3205, 4783008, F3, 22) (dual of [4783008, 4782803, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3205, 4783010, F3, 22) (dual of [4783010, 4782805, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [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(3155, 4782969, F3, 17) (dual of [4782969, 4782814, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(3205, 4783010, F3, 22) (dual of [4783010, 4782805, 23]-code), using
- OOA 4-folding [i] based on linear OA(3205, 4783008, F3, 22) (dual of [4783008, 4782803, 23]-code), using
(205−22, 205, large)-Net in Base 3 — Upper bound on s
There is no (183, 205, large)-net in base 3, because
- 20 times m-reduction [i] would yield (183, 185, large)-net in base 3, but