Best Known (197−21, 197, s)-Nets in Base 3
(197−21, 197, 478298)-Net over F3 — Constructive and digital
Digital (176, 197, 478298)-net over F3, using
- net defined by OOA [i] based on linear OOA(3197, 478298, F3, 21, 21) (dual of [(478298, 21), 10044061, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3197, 4782981, F3, 21) (dual of [4782981, 4782784, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3197, 4782983, F3, 21) (dual of [4782983, 4782786, 22]-code), using
- 1 times truncation [i] based on linear OA(3198, 4782984, F3, 22) (dual of [4782984, 4782786, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [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(3183, 4782969, F3, 20) (dual of [4782969, 4782786, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- 1 times truncation [i] based on linear OA(3198, 4782984, F3, 22) (dual of [4782984, 4782786, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3197, 4782983, F3, 21) (dual of [4782983, 4782786, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3197, 4782981, F3, 21) (dual of [4782981, 4782784, 22]-code), using
(197−21, 197, 1195745)-Net over F3 — Digital
Digital (176, 197, 1195745)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3197, 1195745, F3, 4, 21) (dual of [(1195745, 4), 4782783, 22]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3197, 4782980, F3, 21) (dual of [4782980, 4782783, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3197, 4782983, F3, 21) (dual of [4782983, 4782786, 22]-code), using
- 1 times truncation [i] based on linear OA(3198, 4782984, F3, 22) (dual of [4782984, 4782786, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [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(3183, 4782969, F3, 20) (dual of [4782969, 4782786, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(31, 15, F3, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- 1 times truncation [i] based on linear OA(3198, 4782984, F3, 22) (dual of [4782984, 4782786, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3197, 4782983, F3, 21) (dual of [4782983, 4782786, 22]-code), using
- OOA 4-folding [i] based on linear OA(3197, 4782980, F3, 21) (dual of [4782980, 4782783, 22]-code), using
(197−21, 197, large)-Net in Base 3 — Upper bound on s
There is no (176, 197, large)-net in base 3, because
- 19 times m-reduction [i] would yield (176, 178, large)-net in base 3, but