Best Known (192, 192+40, s)-Nets in Base 2
(192, 192+40, 380)-Net over F2 — Constructive and digital
Digital (192, 232, 380)-net over F2, using
- 22 times duplication [i] based on digital (190, 230, 380)-net over F2, using
- t-expansion [i] based on digital (189, 230, 380)-net over F2, using
- trace code for nets [i] based on digital (5, 46, 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, 46, 76)-net over F32, using
- t-expansion [i] based on digital (189, 230, 380)-net over F2, using
(192, 192+40, 1036)-Net over F2 — Digital
Digital (192, 232, 1036)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2232, 1036, F2, 2, 40) (dual of [(1036, 2), 1840, 41]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2232, 1046, F2, 2, 40) (dual of [(1046, 2), 1860, 41]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2232, 2092, F2, 40) (dual of [2092, 1860, 41]-code), using
- 1 times truncation [i] based on linear OA(2233, 2093, F2, 41) (dual of [2093, 1860, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [i] based on
- linear OA(2221, 2048, F2, 41) (dual of [2048, 1827, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2188, 2048, F2, 35) (dual of [2048, 1860, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(212, 45, F2, 5) (dual of [45, 33, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [i] based on
- 1 times truncation [i] based on linear OA(2233, 2093, F2, 41) (dual of [2093, 1860, 42]-code), using
- OOA 2-folding [i] based on linear OA(2232, 2092, F2, 40) (dual of [2092, 1860, 41]-code), using
- discarding factors / shortening the dual code based on linear OOA(2232, 1046, F2, 2, 40) (dual of [(1046, 2), 1860, 41]-NRT-code), using
(192, 192+40, 25748)-Net in Base 2 — Upper bound on s
There is no (192, 232, 25749)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6902 764591 942347 296368 644271 175377 163382 797395 592319 837181 929429 497081 > 2232 [i]