Best Known (203, 203+42, s)-Nets in Base 2
(203, 203+42, 490)-Net over F2 — Constructive and digital
Digital (203, 245, 490)-net over F2, using
- trace code for nets [i] based on digital (7, 49, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
(203, 203+42, 1047)-Net over F2 — Digital
Digital (203, 245, 1047)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2245, 1047, F2, 2, 42) (dual of [(1047, 2), 1849, 43]-NRT-code), using
- strength reduction [i] based on linear OOA(2245, 1047, F2, 2, 43) (dual of [(1047, 2), 1849, 44]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2245, 2094, F2, 43) (dual of [2094, 1849, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(36) [i] based on
- linear OA(2232, 2048, F2, 43) (dual of [2048, 1816, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2199, 2048, F2, 37) (dual of [2048, 1849, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(213, 46, F2, 5) (dual of [46, 33, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- construction X applied to Ce(42) ⊂ Ce(36) [i] based on
- OOA 2-folding [i] based on linear OA(2245, 2094, F2, 43) (dual of [2094, 1849, 44]-code), using
- strength reduction [i] based on linear OOA(2245, 1047, F2, 2, 43) (dual of [(1047, 2), 1849, 44]-NRT-code), using
(203, 203+42, 28185)-Net in Base 2 — Upper bound on s
There is no (203, 245, 28186)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 56 542977 224382 816305 303913 138622 447393 094297 812082 616051 959922 060022 516798 > 2245 [i]