Best Known (154, 154+26, s)-Nets in Base 2
(154, 154+26, 632)-Net over F2 — Constructive and digital
Digital (154, 180, 632)-net over F2, using
- 24 times duplication [i] based on digital (150, 176, 632)-net over F2, using
- t-expansion [i] based on digital (149, 176, 632)-net over F2, using
- net defined by OOA [i] based on linear OOA(2176, 632, F2, 27, 27) (dual of [(632, 27), 16888, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2176, 8217, F2, 27) (dual of [8217, 8041, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2176, 8224, F2, 27) (dual of [8224, 8048, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2144, 8192, F2, 23) (dual of [8192, 8048, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(26) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(2176, 8224, F2, 27) (dual of [8224, 8048, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2176, 8217, F2, 27) (dual of [8217, 8041, 28]-code), using
- net defined by OOA [i] based on linear OOA(2176, 632, F2, 27, 27) (dual of [(632, 27), 16888, 28]-NRT-code), using
- t-expansion [i] based on digital (149, 176, 632)-net over F2, using
(154, 154+26, 2360)-Net over F2 — Digital
Digital (154, 180, 2360)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2180, 2360, F2, 3, 26) (dual of [(2360, 3), 6900, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2180, 2742, F2, 3, 26) (dual of [(2742, 3), 8046, 27]-NRT-code), using
- 22 times duplication [i] based on linear OOA(2178, 2742, F2, 3, 26) (dual of [(2742, 3), 8048, 27]-NRT-code), using
- strength reduction [i] based on linear OOA(2178, 2742, F2, 3, 27) (dual of [(2742, 3), 8048, 28]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2178, 8226, F2, 27) (dual of [8226, 8048, 28]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2176, 8224, F2, 27) (dual of [8224, 8048, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2144, 8192, F2, 23) (dual of [8192, 8048, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- 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(26) ⊂ Ce(22) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(2176, 8224, F2, 27) (dual of [8224, 8048, 28]-code), using
- OOA 3-folding [i] based on linear OA(2178, 8226, F2, 27) (dual of [8226, 8048, 28]-code), using
- strength reduction [i] based on linear OOA(2178, 2742, F2, 3, 27) (dual of [(2742, 3), 8048, 28]-NRT-code), using
- 22 times duplication [i] based on linear OOA(2178, 2742, F2, 3, 26) (dual of [(2742, 3), 8048, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2180, 2742, F2, 3, 26) (dual of [(2742, 3), 8046, 27]-NRT-code), using
(154, 154+26, 83447)-Net in Base 2 — Upper bound on s
There is no (154, 180, 83448)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 532540 662511 539079 995696 987662 627144 078981 327697 655778 > 2180 [i]