Best Known (30−6, 30, s)-Nets in Base 8
(30−6, 30, 10989)-Net over F8 — Constructive and digital
Digital (24, 30, 10989)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 65)-net over F8, using
- net defined by OOA [i] based on linear OOA(84, 65, F8, 3, 3) (dual of [(65, 3), 191, 4]-NRT-code), using
- digital (20, 26, 10924)-net over F8, using
- net defined by OOA [i] based on linear OOA(826, 10924, F8, 6, 6) (dual of [(10924, 6), 65518, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(826, 32772, F8, 6) (dual of [32772, 32746, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(826, 32773, F8, 6) (dual of [32773, 32747, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(826, 32768, F8, 6) (dual of [32768, 32742, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(821, 32768, F8, 5) (dual of [32768, 32747, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(826, 32773, F8, 6) (dual of [32773, 32747, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(826, 32772, F8, 6) (dual of [32772, 32746, 7]-code), using
- net defined by OOA [i] based on linear OOA(826, 10924, F8, 6, 6) (dual of [(10924, 6), 65518, 7]-NRT-code), using
- digital (1, 4, 65)-net over F8, using
(30−6, 30, 43692)-Net in Base 8 — Constructive
(24, 30, 43692)-net in base 8, using
- net defined by OOA [i] based on OOA(830, 43692, S8, 6, 6), using
- OA 3-folding and stacking [i] based on OA(830, 131076, S8, 6), using
- discarding parts of the base [i] based on linear OA(1622, 131076, F16, 6) (dual of [131076, 131054, 7]-code), using
- trace code [i] based on linear OA(25611, 65538, F256, 6) (dual of [65538, 65527, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2569, 65536, F256, 5) (dual of [65536, 65527, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 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(25611, 65538, F256, 6) (dual of [65538, 65527, 7]-code), using
- discarding parts of the base [i] based on linear OA(1622, 131076, F16, 6) (dual of [131076, 131054, 7]-code), using
- OA 3-folding and stacking [i] based on OA(830, 131076, S8, 6), using
(30−6, 30, 97564)-Net over F8 — Digital
Digital (24, 30, 97564)-net over F8, using
(30−6, 30, large)-Net in Base 8 — Upper bound on s
There is no (24, 30, large)-net in base 8, because
- 4 times m-reduction [i] would yield (24, 26, large)-net in base 8, but