Best Known (117−10, 117, s)-Nets in Base 2
(117−10, 117, 1677720)-Net over F2 — Constructive and digital
Digital (107, 117, 1677720)-net over F2, using
- 21 times duplication [i] based on digital (106, 116, 1677720)-net over F2, using
- t-expansion [i] based on digital (105, 116, 1677720)-net over F2, using
- net defined by OOA [i] based on linear OOA(2116, 1677720, F2, 11, 11) (dual of [(1677720, 11), 18454804, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2116, 8388601, F2, 11) (dual of [8388601, 8388485, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2116, large, F2, 11) (dual of [large, large−116, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(2116, large, F2, 11) (dual of [large, large−116, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2116, 8388601, F2, 11) (dual of [8388601, 8388485, 12]-code), using
- net defined by OOA [i] based on linear OOA(2116, 1677720, F2, 11, 11) (dual of [(1677720, 11), 18454804, 12]-NRT-code), using
- t-expansion [i] based on digital (105, 116, 1677720)-net over F2, using
(117−10, 117, 2097151)-Net over F2 — Digital
Digital (107, 117, 2097151)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2117, 2097151, F2, 4, 10) (dual of [(2097151, 4), 8388487, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2117, 4194302, F2, 2, 10) (dual of [(4194302, 2), 8388487, 11]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2115, 4194301, F2, 2, 10) (dual of [(4194301, 2), 8388487, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2115, 8388602, F2, 10) (dual of [8388602, 8388487, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2115, large, F2, 10) (dual of [large, large−115, 11]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2115, large, F2, 10) (dual of [large, large−115, 11]-code), using
- OOA 2-folding [i] based on linear OA(2115, 8388602, F2, 10) (dual of [8388602, 8388487, 11]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2115, 4194301, F2, 2, 10) (dual of [(4194301, 2), 8388487, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2117, 4194302, F2, 2, 10) (dual of [(4194302, 2), 8388487, 11]-NRT-code), using
(117−10, 117, large)-Net in Base 2 — Upper bound on s
There is no (107, 117, large)-net in base 2, because
- 8 times m-reduction [i] would yield (107, 109, large)-net in base 2, but