Best Known (184−29, 184, s)-Nets in Base 2
(184−29, 184, 586)-Net over F2 — Constructive and digital
Digital (155, 184, 586)-net over F2, using
- net defined by OOA [i] based on linear OOA(2184, 586, F2, 29, 29) (dual of [(586, 29), 16810, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2184, 8205, F2, 29) (dual of [8205, 8021, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, 8206, F2, 29) (dual of [8206, 8022, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2183, 8192, F2, 29) (dual of [8192, 8009, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 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(21, 14, F2, 1) (dual of [14, 13, 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(28) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(2184, 8206, F2, 29) (dual of [8206, 8022, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2184, 8205, F2, 29) (dual of [8205, 8021, 30]-code), using
(184−29, 184, 1740)-Net over F2 — Digital
Digital (155, 184, 1740)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2184, 1740, F2, 4, 29) (dual of [(1740, 4), 6776, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2184, 2051, F2, 4, 29) (dual of [(2051, 4), 8020, 30]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2184, 8204, F2, 29) (dual of [8204, 8020, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, 8206, F2, 29) (dual of [8206, 8022, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2183, 8192, F2, 29) (dual of [8192, 8009, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- 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(21, 14, F2, 1) (dual of [14, 13, 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(28) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(2184, 8206, F2, 29) (dual of [8206, 8022, 30]-code), using
- OOA 4-folding [i] based on linear OA(2184, 8204, F2, 29) (dual of [8204, 8020, 30]-code), using
- discarding factors / shortening the dual code based on linear OOA(2184, 2051, F2, 4, 29) (dual of [(2051, 4), 8020, 30]-NRT-code), using
(184−29, 184, 52021)-Net in Base 2 — Upper bound on s
There is no (155, 184, 52022)-net in base 2, because
- 1 times m-reduction [i] would yield (155, 183, 52022)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 12 263242 986850 680682 438202 973796 374165 290508 682916 897368 > 2183 [i]