Best Known (116−25, 116, s)-Nets in Base 8
(116−25, 116, 2733)-Net over F8 — Constructive and digital
Digital (91, 116, 2733)-net over F8, using
- 83 times duplication [i] based on digital (88, 113, 2733)-net over F8, using
- net defined by OOA [i] based on linear OOA(8113, 2733, F8, 25, 25) (dual of [(2733, 25), 68212, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8113, 32797, F8, 25) (dual of [32797, 32684, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8113, 32800, F8, 25) (dual of [32800, 32687, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(18) [i] based on
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(881, 32768, F8, 19) (dual of [32768, 32687, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(24) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(8113, 32800, F8, 25) (dual of [32800, 32687, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8113, 32797, F8, 25) (dual of [32797, 32684, 26]-code), using
- net defined by OOA [i] based on linear OOA(8113, 2733, F8, 25, 25) (dual of [(2733, 25), 68212, 26]-NRT-code), using
(116−25, 116, 32808)-Net over F8 — Digital
Digital (91, 116, 32808)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8116, 32808, F8, 25) (dual of [32808, 32692, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(876, 32768, F8, 18) (dual of [32768, 32692, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(810, 40, F8, 6) (dual of [40, 30, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- a “GraX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(810, 74, F8, 6) (dual of [74, 64, 7]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
(116−25, 116, large)-Net in Base 8 — Upper bound on s
There is no (91, 116, large)-net in base 8, because
- 23 times m-reduction [i] would yield (91, 93, large)-net in base 8, but