Best Known (93, 93+27, s)-Nets in Base 8
(93, 93+27, 2522)-Net over F8 — Constructive and digital
Digital (93, 120, 2522)-net over F8, using
- net defined by OOA [i] based on linear OOA(8120, 2522, F8, 27, 27) (dual of [(2522, 27), 67974, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8120, 32787, F8, 27) (dual of [32787, 32667, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8101, 32768, F8, 23) (dual of [32768, 32667, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(84, 19, F8, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,8)), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- OOA 13-folding and stacking with additional row [i] based on linear OA(8120, 32787, F8, 27) (dual of [32787, 32667, 28]-code), using
(93, 93+27, 28907)-Net over F8 — Digital
Digital (93, 120, 28907)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8120, 28907, F8, 27) (dual of [28907, 28787, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8120, 32787, F8, 27) (dual of [32787, 32667, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(8101, 32768, F8, 23) (dual of [32768, 32667, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(84, 19, F8, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,8)), using
- construction X applied to Ce(26) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(8120, 32787, F8, 27) (dual of [32787, 32667, 28]-code), using
(93, 93+27, large)-Net in Base 8 — Upper bound on s
There is no (93, 120, large)-net in base 8, because
- 25 times m-reduction [i] would yield (93, 95, large)-net in base 8, but