Best Known (66, 79, s)-Nets in Base 8
(66, 79, 349527)-Net over F8 — Constructive and digital
Digital (66, 79, 349527)-net over F8, using
- net defined by OOA [i] based on linear OOA(879, 349527, F8, 13, 13) (dual of [(349527, 13), 4543772, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(879, 2097163, F8, 13) (dual of [2097163, 2097084, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(879, 2097167, F8, 13) (dual of [2097167, 2097088, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(878, 2097152, F8, 13) (dual of [2097152, 2097074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(864, 2097152, F8, 11) (dual of [2097152, 2097088, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(879, 2097167, F8, 13) (dual of [2097167, 2097088, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(879, 2097163, F8, 13) (dual of [2097163, 2097084, 14]-code), using
(66, 79, 1776821)-Net over F8 — Digital
Digital (66, 79, 1776821)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(879, 1776821, F8, 13) (dual of [1776821, 1776742, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(879, 2097167, F8, 13) (dual of [2097167, 2097088, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(878, 2097152, F8, 13) (dual of [2097152, 2097074, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(864, 2097152, F8, 11) (dual of [2097152, 2097088, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(879, 2097167, F8, 13) (dual of [2097167, 2097088, 14]-code), using
(66, 79, large)-Net in Base 8 — Upper bound on s
There is no (66, 79, large)-net in base 8, because
- 11 times m-reduction [i] would yield (66, 68, large)-net in base 8, but