Best Known (199, 199+38, s)-Nets in Base 2
(199, 199+38, 520)-Net over F2 — Constructive and digital
Digital (199, 237, 520)-net over F2, using
- 22 times duplication [i] based on digital (197, 235, 520)-net over F2, using
- trace code for nets [i] based on digital (9, 47, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- trace code for nets [i] based on digital (9, 47, 104)-net over F32, using
(199, 199+38, 1410)-Net over F2 — Digital
Digital (199, 237, 1410)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2237, 1410, F2, 2, 38) (dual of [(1410, 2), 2583, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2237, 2064, F2, 2, 38) (dual of [(2064, 2), 3891, 39]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2235, 2063, F2, 2, 38) (dual of [(2063, 2), 3891, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2235, 4126, F2, 38) (dual of [4126, 3891, 39]-code), using
- strength reduction [i] based on linear OA(2235, 4126, F2, 39) (dual of [4126, 3891, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(34) [i] based on
- linear OA(2229, 4096, F2, 39) (dual of [4096, 3867, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2205, 4096, F2, 35) (dual of [4096, 3891, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(38) ⊂ Ce(34) [i] based on
- strength reduction [i] based on linear OA(2235, 4126, F2, 39) (dual of [4126, 3891, 40]-code), using
- OOA 2-folding [i] based on linear OA(2235, 4126, F2, 38) (dual of [4126, 3891, 39]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2235, 2063, F2, 2, 38) (dual of [(2063, 2), 3891, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2237, 2064, F2, 2, 38) (dual of [(2064, 2), 3891, 39]-NRT-code), using
(199, 199+38, 45071)-Net in Base 2 — Upper bound on s
There is no (199, 237, 45072)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 220931 797865 792490 167644 473552 642133 795949 624113 673847 778109 161744 447168 > 2237 [i]