Best Known (257−11, 257, s)-Nets in Base 2
(257−11, 257, large)-Net over F2 — Constructive and digital
Digital (246, 257, large)-net over F2, using
- 22 times duplication [i] based on digital (244, 255, large)-net over F2, using
- trace code for nets [i] based on digital (74, 85, 2796201)-net over F8, using
- net defined by OOA [i] based on linear OOA(885, 2796201, F8, 15, 11) (dual of [(2796201, 15), 41942930, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(885, 5592403, F8, 3, 11) (dual of [(5592403, 3), 16777124, 12]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(882, 5592402, F8, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
- trace code [i] based on linear OOA(6441, 2796201, F64, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6441, large, F64, 11) (dual of [large, large−41, 12]-code), using
- trace code [i] based on linear OOA(6441, 2796201, F64, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(882, 5592402, F8, 3, 11) (dual of [(5592402, 3), 16777124, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(885, 5592403, F8, 3, 11) (dual of [(5592403, 3), 16777124, 12]-NRT-code), using
- net defined by OOA [i] based on linear OOA(885, 2796201, F8, 15, 11) (dual of [(2796201, 15), 41942930, 12]-NRT-code), using
- trace code for nets [i] based on digital (74, 85, 2796201)-net over F8, using
(257−11, 257, large)-Net in Base 2 — Upper bound on s
There is no (246, 257, large)-net in base 2, because
- 9 times m-reduction [i] would yield (246, 248, large)-net in base 2, but