Best Known (186, 216, s)-Nets in Base 2
(186, 216, 1094)-Net over F2 — Constructive and digital
Digital (186, 216, 1094)-net over F2, using
- net defined by OOA [i] based on linear OOA(2216, 1094, F2, 30, 30) (dual of [(1094, 30), 32604, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(2216, 16410, F2, 30) (dual of [16410, 16194, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2216, 16415, F2, 30) (dual of [16415, 16199, 31]-code), using
- 1 times truncation [i] based on linear OA(2217, 16416, F2, 31) (dual of [16416, 16199, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(30) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(2217, 16416, F2, 31) (dual of [16416, 16199, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2216, 16415, F2, 30) (dual of [16415, 16199, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(2216, 16410, F2, 30) (dual of [16410, 16194, 31]-code), using
(186, 216, 3597)-Net over F2 — Digital
Digital (186, 216, 3597)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2216, 3597, F2, 4, 30) (dual of [(3597, 4), 14172, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2216, 4103, F2, 4, 30) (dual of [(4103, 4), 16196, 31]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2216, 16412, F2, 30) (dual of [16412, 16196, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2216, 16415, F2, 30) (dual of [16415, 16199, 31]-code), using
- 1 times truncation [i] based on linear OA(2217, 16416, F2, 31) (dual of [16416, 16199, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(30) ⊂ Ce(26) [i] based on
- 1 times truncation [i] based on linear OA(2217, 16416, F2, 31) (dual of [16416, 16199, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2216, 16415, F2, 30) (dual of [16415, 16199, 31]-code), using
- OOA 4-folding [i] based on linear OA(2216, 16412, F2, 30) (dual of [16412, 16196, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(2216, 4103, F2, 4, 30) (dual of [(4103, 4), 16196, 31]-NRT-code), using
(186, 216, 138844)-Net in Base 2 — Upper bound on s
There is no (186, 216, 138845)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 105314 001685 513782 026023 119373 056787 726077 120844 859995 431167 999208 > 2216 [i]