Best Known (184, 184+22, s)-Nets in Base 3
(184, 184+22, 434820)-Net over F3 — Constructive and digital
Digital (184, 206, 434820)-net over F3, using
- net defined by OOA [i] based on linear OOA(3206, 434820, F3, 22, 22) (dual of [(434820, 22), 9565834, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3206, 4783020, F3, 22) (dual of [4783020, 4782814, 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(39, 51, F3, 4) (dual of [51, 42, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- OA 11-folding and stacking [i] based on linear OA(3206, 4783020, F3, 22) (dual of [4783020, 4782814, 23]-code), using
(184, 184+22, 1195755)-Net over F3 — Digital
Digital (184, 206, 1195755)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3206, 1195755, F3, 4, 22) (dual of [(1195755, 4), 4782814, 23]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3206, 4783020, F3, 22) (dual of [4783020, 4782814, 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(39, 51, F3, 4) (dual of [51, 42, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- OOA 4-folding [i] based on linear OA(3206, 4783020, F3, 22) (dual of [4783020, 4782814, 23]-code), using
(184, 184+22, large)-Net in Base 3 — Upper bound on s
There is no (184, 206, large)-net in base 3, because
- 20 times m-reduction [i] would yield (184, 186, large)-net in base 3, but