Best Known (94, 94+26, s)-Nets in Base 8
(94, 94+26, 2523)-Net over F8 — Constructive and digital
Digital (94, 120, 2523)-net over F8, using
- 82 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(8118, 2523, F8, 26, 26) (dual of [(2523, 26), 65480, 27]-NRT-code), using
(94, 94+26, 32804)-Net over F8 — Digital
Digital (94, 120, 32804)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8120, 32804, F8, 26) (dual of [32804, 32684, 27]-code), using
- construction X with 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
- linear OA(8118, 32802, F8, 25) (dual of [32802, 32684, 26]-code), using Gilbert–Varšamov bound and bm = 8118 > Vbs−1(k−1) = 736 762561 909082 604393 811800 266375 984523 760238 003475 094296 858920 330895 985895 776870 511027 824062 597701 751668 [i]
- linear OA(80, 2, F8, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(8118, 32800, F8, 26) (dual of [32800, 32682, 27]-code), using
- construction X with Varšamov bound [i] based on
(94, 94+26, large)-Net in Base 8 — Upper bound on s
There is no (94, 120, large)-net in base 8, because
- 24 times m-reduction [i] would yield (94, 96, large)-net in base 8, but