Best Known (95, 105, s)-Nets in Base 2
(95, 105, 419430)-Net over F2 — Constructive and digital
Digital (95, 105, 419430)-net over F2, using
- net defined by OOA [i] based on linear OOA(2105, 419430, F2, 10, 10) (dual of [(419430, 10), 4194195, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2105, 2097150, F2, 10) (dual of [2097150, 2097045, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2105, 2097151, F2, 10) (dual of [2097151, 2097046, 11]-code), using
- 1 times truncation [i] based on linear OA(2106, 2097152, F2, 11) (dual of [2097152, 2097046, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 1 times truncation [i] based on linear OA(2106, 2097152, F2, 11) (dual of [2097152, 2097046, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2105, 2097151, F2, 10) (dual of [2097151, 2097046, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2105, 2097150, F2, 10) (dual of [2097150, 2097045, 11]-code), using
(95, 105, 524287)-Net over F2 — Digital
Digital (95, 105, 524287)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2105, 524287, F2, 4, 10) (dual of [(524287, 4), 2097043, 11]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2105, 2097148, F2, 10) (dual of [2097148, 2097043, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2105, 2097151, F2, 10) (dual of [2097151, 2097046, 11]-code), using
- 1 times truncation [i] based on linear OA(2106, 2097152, F2, 11) (dual of [2097152, 2097046, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 1 times truncation [i] based on linear OA(2106, 2097152, F2, 11) (dual of [2097152, 2097046, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2105, 2097151, F2, 10) (dual of [2097151, 2097046, 11]-code), using
- OOA 4-folding [i] based on linear OA(2105, 2097148, F2, 10) (dual of [2097148, 2097043, 11]-code), using
(95, 105, 5463432)-Net in Base 2 — Upper bound on s
There is no (95, 105, 5463433)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 40 564828 465292 759287 983246 345428 > 2105 [i]