Best Known (190, 190+42, s)-Nets in Base 2
(190, 190+42, 320)-Net over F2 — Constructive and digital
Digital (190, 232, 320)-net over F2, using
- 22 times duplication [i] based on digital (188, 230, 320)-net over F2, using
- t-expansion [i] based on digital (187, 230, 320)-net over F2, using
- trace code for nets [i] based on digital (3, 46, 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, 46, 64)-net over F32, using
- t-expansion [i] based on digital (187, 230, 320)-net over F2, using
(190, 190+42, 862)-Net over F2 — Digital
Digital (190, 232, 862)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2232, 862, F2, 2, 42) (dual of [(862, 2), 1492, 43]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2232, 1029, F2, 2, 42) (dual of [(1029, 2), 1826, 43]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2232, 2058, F2, 42) (dual of [2058, 1826, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(2232, 2059, F2, 42) (dual of [2059, 1827, 43]-code), using
- 1 times truncation [i] based on linear OA(2233, 2060, F2, 43) (dual of [2060, 1827, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(40) [i] based on
- linear OA(2232, 2048, F2, 43) (dual of [2048, 1816, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- 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(21, 12, F2, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(42) ⊂ Ce(40) [i] based on
- 1 times truncation [i] based on linear OA(2233, 2060, F2, 43) (dual of [2060, 1827, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(2232, 2059, F2, 42) (dual of [2059, 1827, 43]-code), using
- OOA 2-folding [i] based on linear OA(2232, 2058, F2, 42) (dual of [2058, 1826, 43]-code), using
- discarding factors / shortening the dual code based on linear OOA(2232, 1029, F2, 2, 42) (dual of [(1029, 2), 1826, 43]-NRT-code), using
(190, 190+42, 18341)-Net in Base 2 — Upper bound on s
There is no (190, 232, 18342)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6909 169277 504642 672314 842189 781767 313183 938824 791357 164173 735763 998146 > 2232 [i]