Best Known (5, 11, s)-Nets in Base 64
(5, 11, 1366)-Net over F64 — Constructive and digital
Digital (5, 11, 1366)-net over F64, using
- net defined by OOA [i] based on linear OOA(6411, 1366, F64, 6, 6) (dual of [(1366, 6), 8185, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(6411, 4098, F64, 6) (dual of [4098, 4087, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(6411, 4096, F64, 6) (dual of [4096, 4085, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(649, 4096, F64, 5) (dual of [4096, 4087, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 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(6411, 4098, F64, 6) (dual of [4098, 4087, 7]-code), using
(5, 11, 2049)-Net over F64 — Digital
Digital (5, 11, 2049)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(6411, 2049, F64, 2, 6) (dual of [(2049, 2), 4087, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6411, 4098, F64, 6) (dual of [4098, 4087, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(6411, 4096, F64, 6) (dual of [4096, 4085, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(649, 4096, F64, 5) (dual of [4096, 4087, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 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(6411, 4098, F64, 6) (dual of [4098, 4087, 7]-code), using
(5, 11, 120976)-Net in Base 64 — Upper bound on s
There is no (5, 11, 120977)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 73 788743 024296 375888 > 6411 [i]