Best Known (16, 16+6, s)-Nets in Base 8
(16, 16+6, 2732)-Net over F8 — Constructive and digital
Digital (16, 22, 2732)-net over F8, using
- net defined by OOA [i] based on linear OOA(822, 2732, F8, 6, 6) (dual of [(2732, 6), 16370, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(822, 8196, F8, 6) (dual of [8196, 8174, 7]-code), using
- trace code [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
- trace code [i] based on linear OA(6411, 4098, F64, 6) (dual of [4098, 4087, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(822, 8196, F8, 6) (dual of [8196, 8174, 7]-code), using
(16, 16+6, 8196)-Net over F8 — Digital
Digital (16, 22, 8196)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(822, 8196, F8, 6) (dual of [8196, 8174, 7]-code), using
- trace code [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
- trace code [i] based on linear OA(6411, 4098, F64, 6) (dual of [4098, 4087, 7]-code), using
(16, 16+6, 1088792)-Net in Base 8 — Upper bound on s
There is no (16, 22, 1088793)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 73 787116 548587 262136 > 822 [i]