Best Known (11, 22, s)-Nets in Base 128
(11, 22, 3277)-Net over F128 — Constructive and digital
Digital (11, 22, 3277)-net over F128, using
- 1281 times duplication [i] based on digital (10, 21, 3277)-net over F128, using
- net defined by OOA [i] based on linear OOA(12821, 3277, F128, 11, 11) (dual of [(3277, 11), 36026, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(12821, 16386, F128, 11) (dual of [16386, 16365, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(12821, 16384, F128, 11) (dual of [16384, 16363, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(12819, 16384, F128, 10) (dual of [16384, 16365, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- OOA 5-folding and stacking with additional row [i] based on linear OA(12821, 16386, F128, 11) (dual of [16386, 16365, 12]-code), using
- net defined by OOA [i] based on linear OOA(12821, 3277, F128, 11, 11) (dual of [(3277, 11), 36026, 12]-NRT-code), using
(11, 22, 5491)-Net over F128 — Digital
Digital (11, 22, 5491)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12822, 5491, F128, 2, 11) (dual of [(5491, 2), 10960, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12822, 8195, F128, 2, 11) (dual of [(8195, 2), 16368, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12822, 16390, F128, 11) (dual of [16390, 16368, 12]-code), using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- linear OA(12821, 16385, F128, 11) (dual of [16385, 16364, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(12817, 16385, F128, 9) (dual of [16385, 16368, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,5]) ⊂ C([0,4]) [i] based on
- OOA 2-folding [i] based on linear OA(12822, 16390, F128, 11) (dual of [16390, 16368, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(12822, 8195, F128, 2, 11) (dual of [(8195, 2), 16368, 12]-NRT-code), using
(11, 22, large)-Net in Base 128 — Upper bound on s
There is no (11, 22, large)-net in base 128, because
- 9 times m-reduction [i] would yield (11, 13, large)-net in base 128, but