Best Known (131−11, 131, s)-Nets in Base 2
(131−11, 131, 1677797)-Net over F2 — Constructive and digital
Digital (120, 131, 1677797)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (10, 15, 77)-net over F2, using
- 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
(131−11, 131, 2097227)-Net over F2 — Digital
Digital (120, 131, 2097227)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2131, 2097227, F2, 4, 11) (dual of [(2097227, 4), 8388777, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(215, 77, F2, 4, 5) (dual of [(77, 4), 293, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (10, 15, 77)-net over F2, using
- linear OOA(2116, 2097150, F2, 4, 11) (dual of [(2097150, 4), 8388484, 12]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2116, 8388600, F2, 11) (dual of [8388600, 8388484, 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 4-folding [i] based on linear OA(2116, 8388600, F2, 11) (dual of [8388600, 8388484, 12]-code), using
- linear OOA(215, 77, F2, 4, 5) (dual of [(77, 4), 293, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
(131−11, 131, large)-Net in Base 2 — Upper bound on s
There is no (120, 131, large)-net in base 2, because
- 9 times m-reduction [i] would yield (120, 122, large)-net in base 2, but