Best Known (117, 117+32, s)-Nets in Base 8
(117, 117+32, 2050)-Net over F8 — Constructive and digital
Digital (117, 149, 2050)-net over F8, using
- t-expansion [i] based on digital (116, 149, 2050)-net over F8, using
- net defined by OOA [i] based on linear OOA(8149, 2050, F8, 33, 33) (dual of [(2050, 33), 67501, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(8149, 32801, F8, 33) (dual of [32801, 32652, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8148, 32800, F8, 33) (dual of [32800, 32652, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- linear OA(8141, 32768, F8, 33) (dual of [32768, 32627, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(32) ⊂ Ce(26) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(8148, 32800, F8, 33) (dual of [32800, 32652, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(8149, 32801, F8, 33) (dual of [32801, 32652, 34]-code), using
- net defined by OOA [i] based on linear OOA(8149, 2050, F8, 33, 33) (dual of [(2050, 33), 67501, 34]-NRT-code), using
(117, 117+32, 38883)-Net over F8 — Digital
Digital (117, 149, 38883)-net over F8, using
(117, 117+32, large)-Net in Base 8 — Upper bound on s
There is no (117, 149, large)-net in base 8, because
- 30 times m-reduction [i] would yield (117, 119, large)-net in base 8, but