Best Known (118−26, 118, s)-Nets in Base 8
(118−26, 118, 2523)-Net over F8 — Constructive and digital
Digital (92, 118, 2523)-net over F8, using
- net defined by OOA [i] based on linear OOA(8118, 2523, F8, 26, 26) (dual of [(2523, 26), 65480, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8118, 32799, F8, 26) (dual of [32799, 32681, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8118, 32800, F8, 26) (dual of [32800, 32682, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(886, 32768, F8, 20) (dual of [32768, 32682, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(8118, 32800, F8, 26) (dual of [32800, 32682, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(8118, 32799, F8, 26) (dual of [32799, 32681, 27]-code), using
(118−26, 118, 32800)-Net over F8 — Digital
Digital (92, 118, 32800)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8118, 32800, F8, 26) (dual of [32800, 32682, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(886, 32768, F8, 20) (dual of [32768, 32682, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(87, 32, F8, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
(118−26, 118, large)-Net in Base 8 — Upper bound on s
There is no (92, 118, large)-net in base 8, because
- 24 times m-reduction [i] would yield (92, 94, large)-net in base 8, but