Best Known (186, 208, s)-Nets in Base 3
(186, 208, 434821)-Net over F3 — Constructive and digital
Digital (186, 208, 434821)-net over F3, using
- net defined by OOA [i] based on linear OOA(3208, 434821, F3, 22, 22) (dual of [(434821, 22), 9565854, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3208, 4783031, F3, 22) (dual of [4783031, 4782823, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3208, 4783036, F3, 22) (dual of [4783036, 4782828, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [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(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(311, 67, F3, 5) (dual of [67, 56, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3208, 4783036, F3, 22) (dual of [4783036, 4782828, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3208, 4783031, F3, 22) (dual of [4783031, 4782823, 23]-code), using
(186, 208, 1195759)-Net over F3 — Digital
Digital (186, 208, 1195759)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3208, 1195759, F3, 4, 22) (dual of [(1195759, 4), 4782828, 23]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3208, 4783036, F3, 22) (dual of [4783036, 4782828, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [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(3141, 4782969, F3, 16) (dual of [4782969, 4782828, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(311, 67, F3, 5) (dual of [67, 56, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- OOA 4-folding [i] based on linear OA(3208, 4783036, F3, 22) (dual of [4783036, 4782828, 23]-code), using
(186, 208, large)-Net in Base 3 — Upper bound on s
There is no (186, 208, large)-net in base 3, because
- 20 times m-reduction [i] would yield (186, 188, large)-net in base 3, but