Best Known (75, 75+17, s)-Nets in Base 8
(75, 75+17, 32772)-Net over F8 — Constructive and digital
Digital (75, 92, 32772)-net over F8, using
- net defined by OOA [i] based on linear OOA(892, 32772, F8, 17, 17) (dual of [(32772, 17), 557032, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(892, 262177, F8, 17) (dual of [262177, 262085, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(892, 262181, F8, 17) (dual of [262181, 262089, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(885, 262144, F8, 17) (dual of [262144, 262059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(855, 262144, F8, 11) (dual of [262144, 262089, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(87, 37, F8, 5) (dual of [37, 30, 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
- discarding factors / shortening the dual code based on linear OA(892, 262181, F8, 17) (dual of [262181, 262089, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(892, 262177, F8, 17) (dual of [262177, 262085, 18]-code), using
(75, 75+17, 262181)-Net over F8 — Digital
Digital (75, 92, 262181)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(892, 262181, F8, 17) (dual of [262181, 262089, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(10) [i] based on
- linear OA(885, 262144, F8, 17) (dual of [262144, 262059, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(855, 262144, F8, 11) (dual of [262144, 262089, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(87, 37, F8, 5) (dual of [37, 30, 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
(75, 75+17, large)-Net in Base 8 — Upper bound on s
There is no (75, 92, large)-net in base 8, because
- 15 times m-reduction [i] would yield (75, 77, large)-net in base 8, but