Best Known (11−6, 11, s)-Nets in Base 32
(11−6, 11, 342)-Net over F32 — Constructive and digital
Digital (5, 11, 342)-net over F32, using
- net defined by OOA [i] based on linear OOA(3211, 342, F32, 6, 6) (dual of [(342, 6), 2041, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3211, 1026, F32, 6) (dual of [1026, 1015, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(3211, 1024, F32, 6) (dual of [1024, 1013, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(329, 1024, F32, 5) (dual of [1024, 1015, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(3211, 1026, F32, 6) (dual of [1026, 1015, 7]-code), using
(11−6, 11, 513)-Net over F32 — Digital
Digital (5, 11, 513)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3211, 513, F32, 2, 6) (dual of [(513, 2), 1015, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3211, 1026, F32, 6) (dual of [1026, 1015, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(3211, 1024, F32, 6) (dual of [1024, 1013, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(329, 1024, F32, 5) (dual of [1024, 1015, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OOA 2-folding [i] based on linear OA(3211, 1026, F32, 6) (dual of [1026, 1015, 7]-code), using
(11−6, 11, 19358)-Net in Base 32 — Upper bound on s
There is no (5, 11, 19359)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 36029 347846 488388 > 3211 [i]