Best Known (100−22, 100, s)-Nets in Base 8
(100−22, 100, 2981)-Net over F8 — Constructive and digital
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
(100−22, 100, 32792)-Net over F8 — Digital
Digital (78, 100, 32792)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] 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
(100−22, 100, large)-Net in Base 8 — Upper bound on s
There is no (78, 100, large)-net in base 8, because
- 20 times m-reduction [i] would yield (78, 80, large)-net in base 8, but