Best Known (47, 47+13, s)-Nets in Base 8
(47, 47+13, 5465)-Net over F8 — Constructive and digital
Digital (47, 60, 5465)-net over F8, using
- net defined by OOA [i] based on linear OOA(860, 5465, F8, 13, 13) (dual of [(5465, 13), 70985, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(860, 32791, F8, 13) (dual of [32791, 32731, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(860, 32792, F8, 13) (dual of [32792, 32732, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(856, 32768, F8, 13) (dual of [32768, 32712, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(12) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(860, 32792, F8, 13) (dual of [32792, 32732, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(860, 32791, F8, 13) (dual of [32791, 32731, 14]-code), using
(47, 47+13, 32792)-Net over F8 — Digital
Digital (47, 60, 32792)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(860, 32792, F8, 13) (dual of [32792, 32732, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(856, 32768, F8, 13) (dual of [32768, 32712, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(12) ⊂ Ce(8) [i] based on
(47, 47+13, large)-Net in Base 8 — Upper bound on s
There is no (47, 60, large)-net in base 8, because
- 11 times m-reduction [i] would yield (47, 49, large)-net in base 8, but