Best Known (203, 203+44, s)-Nets in Base 2
(203, 203+44, 380)-Net over F2 — Constructive and digital
Digital (203, 247, 380)-net over F2, using
- 22 times duplication [i] based on digital (201, 245, 380)-net over F2, using
- trace code for nets [i] based on digital (5, 49, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- trace code for nets [i] based on digital (5, 49, 76)-net over F32, using
(203, 203+44, 957)-Net over F2 — Digital
Digital (203, 247, 957)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2247, 957, F2, 2, 44) (dual of [(957, 2), 1667, 45]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2247, 1032, F2, 2, 44) (dual of [(1032, 2), 1817, 45]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2247, 2064, F2, 44) (dual of [2064, 1817, 45]-code), using
- 1 times truncation [i] based on linear OA(2248, 2065, F2, 45) (dual of [2065, 1817, 46]-code), using
- construction X applied to C([0,22]) ⊂ C([0,20]) [i] based on
- linear OA(2243, 2049, F2, 45) (dual of [2049, 1806, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (BCH-bound) [i]
- linear OA(2221, 2049, F2, 41) (dual of [2049, 1828, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
- construction X applied to C([0,22]) ⊂ C([0,20]) [i] based on
- 1 times truncation [i] based on linear OA(2248, 2065, F2, 45) (dual of [2065, 1817, 46]-code), using
- OOA 2-folding [i] based on linear OA(2247, 2064, F2, 44) (dual of [2064, 1817, 45]-code), using
- discarding factors / shortening the dual code based on linear OOA(2247, 1032, F2, 2, 44) (dual of [(1032, 2), 1817, 45]-NRT-code), using
(203, 203+44, 21674)-Net in Base 2 — Upper bound on s
There is no (203, 247, 21675)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 226 276500 642165 372937 859339 457802 315588 394067 833069 099087 504540 996049 659516 > 2247 [i]