Best Known (201, 239, s)-Nets in Base 4
(201, 239, 3452)-Net over F4 — Constructive and digital
Digital (201, 239, 3452)-net over F4, using
- 41 times duplication [i] based on digital (200, 238, 3452)-net over F4, using
- net defined by OOA [i] based on linear OOA(4238, 3452, F4, 38, 38) (dual of [(3452, 38), 130938, 39]-NRT-code), using
- OA 19-folding and stacking [i] based on linear OA(4238, 65588, F4, 38) (dual of [65588, 65350, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(4238, 65589, F4, 38) (dual of [65589, 65351, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(30) [i] based on
- linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(413, 53, F4, 6) (dual of [53, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to Ce(37) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(4238, 65589, F4, 38) (dual of [65589, 65351, 39]-code), using
- OA 19-folding and stacking [i] based on linear OA(4238, 65588, F4, 38) (dual of [65588, 65350, 39]-code), using
- net defined by OOA [i] based on linear OOA(4238, 3452, F4, 38, 38) (dual of [(3452, 38), 130938, 39]-NRT-code), using
(201, 239, 45460)-Net over F4 — Digital
Digital (201, 239, 45460)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4239, 45460, F4, 38) (dual of [45460, 45221, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(4239, 65590, F4, 38) (dual of [65590, 65351, 39]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4238, 65589, F4, 38) (dual of [65589, 65351, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(30) [i] based on
- linear OA(4225, 65536, F4, 38) (dual of [65536, 65311, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(413, 53, F4, 6) (dual of [53, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to Ce(37) ⊂ Ce(30) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4238, 65589, F4, 38) (dual of [65589, 65351, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(4239, 65590, F4, 38) (dual of [65590, 65351, 39]-code), using
(201, 239, large)-Net in Base 4 — Upper bound on s
There is no (201, 239, large)-net in base 4, because
- 36 times m-reduction [i] would yield (201, 203, large)-net in base 4, but