Best Known (235, 260, s)-Nets in Base 2
(235, 260, 174766)-Net over F2 — Constructive and digital
Digital (235, 260, 174766)-net over F2, using
- net defined by OOA [i] based on linear OOA(2260, 174766, F2, 25, 25) (dual of [(174766, 25), 4368890, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2260, 2097193, F2, 25) (dual of [2097193, 2096933, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2260, 2097202, F2, 25) (dual of [2097202, 2096942, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2253, 2097153, F2, 25) (dual of [2097153, 2096900, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2211, 2097153, F2, 21) (dual of [2097153, 2096942, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(27, 49, F2, 3) (dual of [49, 42, 4]-code or 49-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2260, 2097202, F2, 25) (dual of [2097202, 2096942, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2260, 2097193, F2, 25) (dual of [2097193, 2096933, 26]-code), using
(235, 260, 262150)-Net over F2 — Digital
Digital (235, 260, 262150)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2260, 262150, F2, 8, 25) (dual of [(262150, 8), 2096940, 26]-NRT-code), using
- OOA 8-folding [i] based on linear OA(2260, 2097200, F2, 25) (dual of [2097200, 2096940, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2260, 2097202, F2, 25) (dual of [2097202, 2096942, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2253, 2097153, F2, 25) (dual of [2097153, 2096900, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2211, 2097153, F2, 21) (dual of [2097153, 2096942, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(27, 49, F2, 3) (dual of [49, 42, 4]-code or 49-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2260, 2097202, F2, 25) (dual of [2097202, 2096942, 26]-code), using
- OOA 8-folding [i] based on linear OA(2260, 2097200, F2, 25) (dual of [2097200, 2096940, 26]-code), using
(235, 260, large)-Net in Base 2 — Upper bound on s
There is no (235, 260, large)-net in base 2, because
- 23 times m-reduction [i] would yield (235, 237, large)-net in base 2, but