Best Known (72, 92, s)-Nets in Base 8
(72, 92, 3279)-Net over F8 — Constructive and digital
Digital (72, 92, 3279)-net over F8, using
- net defined by OOA [i] based on linear OOA(892, 3279, F8, 20, 20) (dual of [(3279, 20), 65488, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(892, 32790, F8, 20) (dual of [32790, 32698, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(892, 32794, F8, 20) (dual of [32794, 32702, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- 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(866, 32768, F8, 15) (dual of [32768, 32702, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(19) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(892, 32794, F8, 20) (dual of [32794, 32702, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(892, 32790, F8, 20) (dual of [32790, 32698, 21]-code), using
(72, 92, 32794)-Net over F8 — Digital
Digital (72, 92, 32794)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(892, 32794, F8, 20) (dual of [32794, 32702, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(14) [i] based on
- 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(866, 32768, F8, 15) (dual of [32768, 32702, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(19) ⊂ Ce(14) [i] based on
(72, 92, large)-Net in Base 8 — Upper bound on s
There is no (72, 92, large)-net in base 8, because
- 18 times m-reduction [i] would yield (72, 74, large)-net in base 8, but