Best Known (186, 207, s)-Nets in Base 3
(186, 207, 478303)-Net over F3 — Constructive and digital
Digital (186, 207, 478303)-net over F3, using
- 31 times duplication [i] based on digital (185, 206, 478303)-net over F3, using
- net defined by OOA [i] based on linear OOA(3206, 478303, F3, 21, 21) (dual of [(478303, 21), 10044157, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3206, 4783031, F3, 21) (dual of [4783031, 4782825, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3206, 4783034, F3, 21) (dual of [4783034, 4782828, 22]-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(39, 65, F3, 4) (dual of [65, 56, 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(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3206, 4783034, F3, 21) (dual of [4783034, 4782828, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3206, 4783031, F3, 21) (dual of [4783031, 4782825, 22]-code), using
- net defined by OOA [i] based on linear OOA(3206, 478303, F3, 21, 21) (dual of [(478303, 21), 10044157, 22]-NRT-code), using
(186, 207, 1594345)-Net over F3 — Digital
Digital (186, 207, 1594345)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3207, 1594345, F3, 3, 21) (dual of [(1594345, 3), 4782828, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3207, 4783035, F3, 21) (dual of [4783035, 4782828, 22]-code), using
- 1 times truncation [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
- 1 times truncation [i] based on linear OA(3208, 4783036, F3, 22) (dual of [4783036, 4782828, 23]-code), using
- OOA 3-folding [i] based on linear OA(3207, 4783035, F3, 21) (dual of [4783035, 4782828, 22]-code), using
(186, 207, large)-Net in Base 3 — Upper bound on s
There is no (186, 207, large)-net in base 3, because
- 19 times m-reduction [i] would yield (186, 188, large)-net in base 3, but