Best Known (80, 80+22, s)-Nets in Base 8
(80, 80+22, 2981)-Net over F8 — Constructive and digital
Digital (80, 102, 2981)-net over F8, using
- 82 times duplication [i] based on digital (78, 100, 2981)-net over F8, using
- net defined by OOA [i] based on linear OOA(8100, 2981, F8, 22, 22) (dual of [(2981, 22), 65482, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8100, 32791, F8, 22) (dual of [32791, 32691, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8100, 32792, F8, 22) (dual of [32792, 32692, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(876, 32768, F8, 18) (dual of [32768, 32692, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(84, 24, F8, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,8)), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(8100, 32792, F8, 22) (dual of [32792, 32692, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8100, 32791, F8, 22) (dual of [32791, 32691, 23]-code), using
- net defined by OOA [i] based on linear OOA(8100, 2981, F8, 22, 22) (dual of [(2981, 22), 65482, 23]-NRT-code), using
(80, 80+22, 32799)-Net over F8 — Digital
Digital (80, 102, 32799)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8102, 32799, F8, 22) (dual of [32799, 32697, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(871, 32768, F8, 17) (dual of [32768, 32697, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(86, 31, F8, 4) (dual of [31, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- 1 times truncation [i] based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(86, 56, F8, 4) (dual of [56, 50, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
(80, 80+22, large)-Net in Base 8 — Upper bound on s
There is no (80, 102, large)-net in base 8, because
- 20 times m-reduction [i] would yield (80, 82, large)-net in base 8, but