Best Known (134, 151, s)-Nets in Base 2
(134, 151, 32772)-Net over F2 — Constructive and digital
Digital (134, 151, 32772)-net over F2, using
- net defined by OOA [i] based on linear OOA(2151, 32772, F2, 17, 17) (dual of [(32772, 17), 556973, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2151, 262177, F2, 17) (dual of [262177, 262026, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2145, 262145, F2, 17) (dual of [262145, 262000, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2109, 262145, F2, 13) (dual of [262145, 262036, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [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 C([0,8]) ⊂ C([0,6]) [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(2151, 262177, F2, 17) (dual of [262177, 262026, 18]-code), using
(134, 151, 48570)-Net over F2 — Digital
Digital (134, 151, 48570)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2151, 48570, F2, 5, 17) (dual of [(48570, 5), 242699, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2151, 52435, F2, 5, 17) (dual of [(52435, 5), 262024, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2151, 262175, F2, 17) (dual of [262175, 262024, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2151, 262177, F2, 17) (dual of [262177, 262026, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2145, 262145, F2, 17) (dual of [262145, 262000, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2109, 262145, F2, 13) (dual of [262145, 262036, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [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 C([0,8]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2151, 262177, F2, 17) (dual of [262177, 262026, 18]-code), using
- OOA 5-folding [i] based on linear OA(2151, 262175, F2, 17) (dual of [262175, 262024, 18]-code), using
- discarding factors / shortening the dual code based on linear OOA(2151, 52435, F2, 5, 17) (dual of [(52435, 5), 262024, 18]-NRT-code), using
(134, 151, 1659584)-Net in Base 2 — Upper bound on s
There is no (134, 151, 1659585)-net in base 2, because
- 1 times m-reduction [i] would yield (134, 150, 1659585)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1427 248379 306993 265022 327119 902780 689856 840488 > 2150 [i]