Best Known (64, 64+18, s)-Nets in Base 8
(64, 64+18, 3643)-Net over F8 — Constructive and digital
Digital (64, 82, 3643)-net over F8, using
- 82 times duplication [i] based on digital (62, 80, 3643)-net over F8, using
- net defined by OOA [i] based on linear OOA(880, 3643, F8, 18, 18) (dual of [(3643, 18), 65494, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(880, 32787, F8, 18) (dual of [32787, 32707, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(13) [i] based on
- 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(861, 32768, F8, 14) (dual of [32768, 32707, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(17) ⊂ Ce(13) [i] based on
- OA 9-folding and stacking [i] based on linear OA(880, 32787, F8, 18) (dual of [32787, 32707, 19]-code), using
- net defined by OOA [i] based on linear OOA(880, 3643, F8, 18, 18) (dual of [(3643, 18), 65494, 19]-NRT-code), using
(64, 64+18, 32794)-Net over F8 — Digital
Digital (64, 82, 32794)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(882, 32794, F8, 18) (dual of [32794, 32712, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- 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(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(86, 26, F8, 4) (dual of [26, 20, 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(17) ⊂ Ce(12) [i] based on
(64, 64+18, large)-Net in Base 8 — Upper bound on s
There is no (64, 82, large)-net in base 8, because
- 16 times m-reduction [i] would yield (64, 66, large)-net in base 8, but