Best Known (76, 90, s)-Nets in Base 8
(76, 90, 299597)-Net over F8 — Constructive and digital
Digital (76, 90, 299597)-net over F8, using
- 81 times duplication [i] based on digital (75, 89, 299597)-net over F8, using
- net defined by OOA [i] based on linear OOA(889, 299597, F8, 14, 14) (dual of [(299597, 14), 4194269, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(889, 2097179, F8, 14) (dual of [2097179, 2097090, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(889, 2097184, F8, 14) (dual of [2097184, 2097095, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(857, 2097152, F8, 10) (dual of [2097152, 2097095, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(889, 2097184, F8, 14) (dual of [2097184, 2097095, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(889, 2097179, F8, 14) (dual of [2097179, 2097090, 15]-code), using
- net defined by OOA [i] based on linear OOA(889, 299597, F8, 14, 14) (dual of [(299597, 14), 4194269, 15]-NRT-code), using
(76, 90, 2097186)-Net over F8 — Digital
Digital (76, 90, 2097186)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(890, 2097186, F8, 14) (dual of [2097186, 2097096, 15]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(889, 2097184, F8, 14) (dual of [2097184, 2097095, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(885, 2097152, F8, 14) (dual of [2097152, 2097067, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(857, 2097152, F8, 10) (dual of [2097152, 2097095, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(84, 32, F8, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,8)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(889, 2097185, F8, 13) (dual of [2097185, 2097096, 14]-code), using Gilbert–Varšamov bound and bm = 889 > Vbs−1(k−1) = 209153 256979 370980 713353 716128 780870 542763 775821 923133 679432 808138 524142 929933 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 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
- linear OA(889, 2097184, F8, 14) (dual of [2097184, 2097095, 15]-code), using
- construction X with Varšamov bound [i] based on
(76, 90, large)-Net in Base 8 — Upper bound on s
There is no (76, 90, large)-net in base 8, because
- 12 times m-reduction [i] would yield (76, 78, large)-net in base 8, but