Best Known (113, 113+30, s)-Nets in Base 8
(113, 113+30, 2187)-Net over F8 — Constructive and digital
Digital (113, 143, 2187)-net over F8, using
- 1 times m-reduction [i] based on digital (113, 144, 2187)-net over F8, using
- net defined by OOA [i] based on linear OOA(8144, 2187, F8, 31, 31) (dual of [(2187, 31), 67653, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(8144, 32806, F8, 31) (dual of [32806, 32662, 32]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8143, 32805, F8, 31) (dual of [32805, 32662, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(8136, 32768, F8, 31) (dual of [32768, 32632, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(87, 37, F8, 5) (dual of [37, 30, 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(30) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(8143, 32805, F8, 31) (dual of [32805, 32662, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(8144, 32806, F8, 31) (dual of [32806, 32662, 32]-code), using
- net defined by OOA [i] based on linear OOA(8144, 2187, F8, 31, 31) (dual of [(2187, 31), 67653, 32]-NRT-code), using
(113, 113+30, 47350)-Net over F8 — Digital
Digital (113, 143, 47350)-net over F8, using
(113, 113+30, large)-Net in Base 8 — Upper bound on s
There is no (113, 143, large)-net in base 8, because
- 28 times m-reduction [i] would yield (113, 115, large)-net in base 8, but