Best Known (84−15, 84, s)-Nets in Base 8
(84−15, 84, 37453)-Net over F8 — Constructive and digital
Digital (69, 84, 37453)-net over F8, using
- 81 times duplication [i] based on digital (68, 83, 37453)-net over F8, using
- net defined by OOA [i] based on linear OOA(883, 37453, F8, 15, 15) (dual of [(37453, 15), 561712, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(883, 262172, F8, 15) (dual of [262172, 262089, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(879, 262144, F8, 15) (dual of [262144, 262065, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(84, 28, F8, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,8)), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- OOA 7-folding and stacking with additional row [i] based on linear OA(883, 262172, F8, 15) (dual of [262172, 262089, 16]-code), using
- net defined by OOA [i] based on linear OOA(883, 37453, F8, 15, 15) (dual of [(37453, 15), 561712, 16]-NRT-code), using
(84−15, 84, 262174)-Net over F8 — Digital
Digital (69, 84, 262174)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(884, 262174, F8, 15) (dual of [262174, 262090, 16]-code), using
- construction XX applied to Ce(14) ⊂ Ce(10) ⊂ Ce(9) [i] based on
- linear OA(879, 262144, F8, 15) (dual of [262144, 262065, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(849, 262144, F8, 10) (dual of [262144, 262095, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(84, 29, F8, 3) (dual of [29, 25, 4]-code or 29-cap in PG(3,8)), using
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(14) ⊂ Ce(10) ⊂ Ce(9) [i] based on
(84−15, 84, large)-Net in Base 8 — Upper bound on s
There is no (69, 84, large)-net in base 8, because
- 13 times m-reduction [i] would yield (69, 71, large)-net in base 8, but