Best Known (83, 83+15, s)-Nets in Base 2
(83, 83+15, 1174)-Net over F2 — Constructive and digital
Digital (83, 98, 1174)-net over F2, using
- net defined by OOA [i] based on linear OOA(298, 1174, F2, 15, 15) (dual of [(1174, 15), 17512, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(298, 8219, F2, 15) (dual of [8219, 8121, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(298, 8224, F2, 15) (dual of [8224, 8126, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(292, 8192, F2, 15) (dual of [8192, 8100, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(266, 8192, F2, 11) (dual of [8192, 8126, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(14) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(298, 8224, F2, 15) (dual of [8224, 8126, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(298, 8219, F2, 15) (dual of [8219, 8121, 16]-code), using
(83, 83+15, 2056)-Net over F2 — Digital
Digital (83, 98, 2056)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(298, 2056, F2, 4, 15) (dual of [(2056, 4), 8126, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(298, 8224, F2, 15) (dual of [8224, 8126, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(292, 8192, F2, 15) (dual of [8192, 8100, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(266, 8192, F2, 11) (dual of [8192, 8126, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(14) ⊂ Ce(10) [i] based on
- OOA 4-folding [i] based on linear OA(298, 8224, F2, 15) (dual of [8224, 8126, 16]-code), using
(83, 83+15, 50147)-Net in Base 2 — Upper bound on s
There is no (83, 98, 50148)-net in base 2, because
- 1 times m-reduction [i] would yield (83, 97, 50148)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 158471 397624 770881 180611 315448 > 297 [i]