Best Known (190, 229, s)-Nets in Base 2
(190, 229, 380)-Net over F2 — Constructive and digital
Digital (190, 229, 380)-net over F2, using
- t-expansion [i] based on digital (189, 229, 380)-net over F2, using
- 1 times m-reduction [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
- 1 times m-reduction [i] based on digital (189, 230, 380)-net over F2, using
(190, 229, 1171)-Net over F2 — Digital
Digital (190, 229, 1171)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2229, 1171, F2, 3, 39) (dual of [(1171, 3), 3284, 40]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2229, 1365, F2, 3, 39) (dual of [(1365, 3), 3866, 40]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2229, 4095, F2, 39) (dual of [4095, 3866, 40]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2229, 4096, F2, 39) (dual of [4096, 3867, 40]-code), using
- OOA 3-folding [i] based on linear OA(2229, 4095, F2, 39) (dual of [4095, 3866, 40]-code), using
- discarding factors / shortening the dual code based on linear OOA(2229, 1365, F2, 3, 39) (dual of [(1365, 3), 3866, 40]-NRT-code), using
(190, 229, 32448)-Net in Base 2 — Upper bound on s
There is no (190, 229, 32449)-net in base 2, because
- 1 times m-reduction [i] would yield (190, 228, 32449)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 431 364884 459799 427001 648536 455370 675402 727139 281466 239793 742931 483552 > 2228 [i]