Best Known (15, 26, s)-Nets in Base 256
(15, 26, 13364)-Net over F256 — Constructive and digital
Digital (15, 26, 13364)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, 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 (0, 5, 257)-net over F256, using
(15, 26, 65795)-Net over F256 — Digital
Digital (15, 26, 65795)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25626, 65795, F256, 11) (dual of [65795, 65769, 12]-code), using
- (u, u+v)-construction [i] based on
- linear OA(2565, 257, F256, 5) (dual of [257, 252, 6]-code or 257-arc in PG(4,256)), using
- extended Reed–Solomon code RSe(252,256) [i]
- the expurgated narrow-sense BCH-code C(I) with length 257 | 2562−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- algebraic-geometric code AG(F, Q+124P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using the rational function field F256(x) [i]
- algebraic-geometric code AG(F, Q+83P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- algebraic-geometric code AG(F, Q+49P) with degQ = 6 and degPÂ =Â 5 [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257 (see above)
- 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
- linear OA(2565, 257, F256, 5) (dual of [257, 252, 6]-code or 257-arc in PG(4,256)), using
- (u, u+v)-construction [i] based on
(15, 26, large)-Net in Base 256 — Upper bound on s
There is no (15, 26, large)-net in base 256, because
- 9 times m-reduction [i] would yield (15, 17, large)-net in base 256, but