Best Known (17, 17+11, s)-Nets in Base 256
(17, 17+11, 26214)-Net over F256 — Constructive and digital
Digital (17, 28, 26214)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 32640)-net over F256, using
- net defined by OOA [i] based on linear OOA(2567, 32640, F256, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- net defined by OOA [i] based on linear OOA(2567, 32640, F256, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
- digital (10, 21, 13107)-net over F256, using
- net defined by OOA [i] based on linear OOA(25621, 13107, F256, 11, 11) (dual of [(13107, 11), 144156, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 5-folding and stacking with additional row [i] based on linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using
- net defined by OOA [i] based on linear OOA(25621, 13107, F256, 11, 11) (dual of [(13107, 11), 144156, 12]-NRT-code), using
- digital (2, 7, 32640)-net over F256, using
(17, 17+11, 130819)-Net over F256 — Digital
Digital (17, 28, 130819)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25628, 130819, F256, 11) (dual of [130819, 130791, 12]-code), using
- (u, u+v)-construction [i] based on
- linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- linear OA(25621, 65538, F256, 11) (dual of [65538, 65517, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- (u, u+v)-construction [i] based on
(17, 17+11, large)-Net in Base 256 — Upper bound on s
There is no (17, 28, large)-net in base 256, because
- 9 times m-reduction [i] would yield (17, 19, large)-net in base 256, but