Best Known (120, 120+13, s)-Nets in Base 2
(120, 120+13, 699050)-Net over F2 — Constructive and digital
Digital (120, 133, 699050)-net over F2, using
- net defined by OOA [i] based on linear OOA(2133, 699050, F2, 13, 13) (dual of [(699050, 13), 9087517, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2133, 4194301, F2, 13) (dual of [4194301, 4194168, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2133, 4194304, F2, 13) (dual of [4194304, 4194171, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2133, 4194304, F2, 13) (dual of [4194304, 4194171, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2133, 4194301, F2, 13) (dual of [4194301, 4194168, 14]-code), using
(120, 120+13, 838861)-Net over F2 — Digital
Digital (120, 133, 838861)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2133, 838861, F2, 5, 13) (dual of [(838861, 5), 4194172, 14]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2133, 4194305, F2, 13) (dual of [4194305, 4194172, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4194305 | 244−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- OOA 5-folding [i] based on linear OA(2133, 4194305, F2, 13) (dual of [4194305, 4194172, 14]-code), using
(120, 120+13, large)-Net in Base 2 — Upper bound on s
There is no (120, 133, large)-net in base 2, because
- 11 times m-reduction [i] would yield (120, 122, large)-net in base 2, but