Best Known (73, 73+20, s)-Nets in Base 8
(73, 73+20, 3280)-Net over F8 — Constructive and digital
Digital (73, 93, 3280)-net over F8, using
- net defined by OOA [i] based on linear OOA(893, 3280, F8, 20, 20) (dual of [(3280, 20), 65507, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(893, 32800, F8, 20) (dual of [32800, 32707, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [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(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(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(19) ⊂ Ce(13) [i] based on
- OA 10-folding and stacking [i] based on linear OA(893, 32800, F8, 20) (dual of [32800, 32707, 21]-code), using
(73, 73+20, 32800)-Net over F8 — Digital
Digital (73, 93, 32800)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(893, 32800, F8, 20) (dual of [32800, 32707, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [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(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(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(19) ⊂ Ce(13) [i] based on
(73, 73+20, large)-Net in Base 8 — Upper bound on s
There is no (73, 93, large)-net in base 8, because
- 18 times m-reduction [i] would yield (73, 75, large)-net in base 8, but