Best Known (162, 162+36, s)-Nets in Base 2
(162, 162+36, 320)-Net over F2 — Constructive and digital
Digital (162, 198, 320)-net over F2, using
- 23 times duplication [i] based on digital (159, 195, 320)-net over F2, using
- trace code for nets [i] based on digital (3, 39, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- trace code for nets [i] based on digital (3, 39, 64)-net over F32, using
(162, 162+36, 761)-Net over F2 — Digital
Digital (162, 198, 761)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2198, 761, F2, 2, 36) (dual of [(761, 2), 1324, 37]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2198, 1024, F2, 2, 36) (dual of [(1024, 2), 1850, 37]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2198, 2048, F2, 36) (dual of [2048, 1850, 37]-code), using
- 1 times truncation [i] based on linear OA(2199, 2049, F2, 37) (dual of [2049, 1850, 38]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2199, 2049, F2, 37) (dual of [2049, 1850, 38]-code), using
- OOA 2-folding [i] based on linear OA(2198, 2048, F2, 36) (dual of [2048, 1850, 37]-code), using
- discarding factors / shortening the dual code based on linear OOA(2198, 1024, F2, 2, 36) (dual of [(1024, 2), 1850, 37]-NRT-code), using
(162, 162+36, 15442)-Net in Base 2 — Upper bound on s
There is no (162, 198, 15443)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 401995 819674 680550 870765 537996 929696 831135 839885 819900 060009 > 2198 [i]