Best Known (89, 89+16, s)-Nets in Base 8
(89, 89+16, 262149)-Net over F8 — Constructive and digital
Digital (89, 105, 262149)-net over F8, using
- net defined by OOA [i] based on linear OOA(8105, 262149, F8, 16, 16) (dual of [(262149, 16), 4194279, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(8105, 2097192, F8, 16) (dual of [2097192, 2097087, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(8105, 2097193, F8, 16) (dual of [2097193, 2097088, 17]-code), using
- 1 times truncation [i] based on linear OA(8106, 2097194, F8, 17) (dual of [2097194, 2097088, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(87, 42, F8, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(8106, 2097194, F8, 17) (dual of [2097194, 2097088, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(8105, 2097193, F8, 16) (dual of [2097193, 2097088, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(8105, 2097192, F8, 16) (dual of [2097192, 2097087, 17]-code), using
(89, 89+16, 2097193)-Net over F8 — Digital
Digital (89, 105, 2097193)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8105, 2097193, F8, 16) (dual of [2097193, 2097088, 17]-code), using
- 1 times truncation [i] based on linear OA(8106, 2097194, F8, 17) (dual of [2097194, 2097088, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(87, 42, F8, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(8106, 2097194, F8, 17) (dual of [2097194, 2097088, 18]-code), using
(89, 89+16, large)-Net in Base 8 — Upper bound on s
There is no (89, 105, large)-net in base 8, because
- 14 times m-reduction [i] would yield (89, 91, large)-net in base 8, but