Best Known (116, 116+35, s)-Nets in Base 8
(116, 116+35, 1927)-Net over F8 — Constructive and digital
Digital (116, 151, 1927)-net over F8, using
- net defined by OOA [i] based on linear OOA(8151, 1927, F8, 35, 35) (dual of [(1927, 35), 67294, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(8151, 32760, F8, 35) (dual of [32760, 32609, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(8151, 32768, F8, 35) (dual of [32768, 32617, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(8151, 32768, F8, 35) (dual of [32768, 32617, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(8151, 32760, F8, 35) (dual of [32760, 32609, 36]-code), using
(116, 116+35, 23925)-Net over F8 — Digital
Digital (116, 151, 23925)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8151, 23925, F8, 35) (dual of [23925, 23774, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(8151, 32768, F8, 35) (dual of [32768, 32617, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(8151, 32768, F8, 35) (dual of [32768, 32617, 36]-code), using
(116, 116+35, large)-Net in Base 8 — Upper bound on s
There is no (116, 151, large)-net in base 8, because
- 33 times m-reduction [i] would yield (116, 118, large)-net in base 8, but