Best Known (103, 116, s)-Nets in Base 2
(103, 116, 87384)-Net over F2 — Constructive and digital
Digital (103, 116, 87384)-net over F2, using
- net defined by OOA [i] based on linear OOA(2116, 87384, F2, 13, 13) (dual of [(87384, 13), 1135876, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2116, 524305, F2, 13) (dual of [524305, 524189, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2116, 524308, F2, 13) (dual of [524308, 524192, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(2115, 524288, F2, 13) (dual of [524288, 524173, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(296, 524288, F2, 11) (dual of [524288, 524192, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(2116, 524308, F2, 13) (dual of [524308, 524192, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2116, 524305, F2, 13) (dual of [524305, 524189, 14]-code), using
(103, 116, 104861)-Net over F2 — Digital
Digital (103, 116, 104861)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2116, 104861, F2, 5, 13) (dual of [(104861, 5), 524189, 14]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2116, 524305, F2, 13) (dual of [524305, 524189, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2116, 524308, F2, 13) (dual of [524308, 524192, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(2115, 524288, F2, 13) (dual of [524288, 524173, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(296, 524288, F2, 11) (dual of [524288, 524192, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(2116, 524308, F2, 13) (dual of [524308, 524192, 14]-code), using
- OOA 5-folding [i] based on linear OA(2116, 524305, F2, 13) (dual of [524305, 524189, 14]-code), using
(103, 116, 1761820)-Net in Base 2 — Upper bound on s
There is no (103, 116, 1761821)-net in base 2, because
- 1 times m-reduction [i] would yield (103, 115, 1761821)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 41538 496080 521946 599991 772819 309432 > 2115 [i]