Best Known (24, 32, s)-Nets in Base 8
(24, 32, 2050)-Net over F8 — Constructive and digital
Digital (24, 32, 2050)-net over F8, using
- net defined by OOA [i] based on linear OOA(832, 2050, F8, 8, 8) (dual of [(2050, 8), 16368, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(832, 8200, F8, 8) (dual of [8200, 8168, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(832, 8202, F8, 8) (dual of [8202, 8170, 9]-code), using
- trace code [i] based on linear OA(6416, 4101, F64, 8) (dual of [4101, 4085, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(6416, 4101, F64, 8) (dual of [4101, 4085, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(832, 8202, F8, 8) (dual of [8202, 8170, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(832, 8200, F8, 8) (dual of [8200, 8168, 9]-code), using
(24, 32, 8202)-Net over F8 — Digital
Digital (24, 32, 8202)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(832, 8202, F8, 8) (dual of [8202, 8170, 9]-code), using
- trace code [i] based on linear OA(6416, 4101, F64, 8) (dual of [4101, 4085, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(6416, 4101, F64, 8) (dual of [4101, 4085, 9]-code), using
(24, 32, 5304866)-Net in Base 8 — Upper bound on s
There is no (24, 32, 5304867)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 79228 164902 019098 425948 792872 > 832 [i]