Best Known (148−32, 148, s)-Nets in Base 8
(148−32, 148, 2050)-Net over F8 — Constructive and digital
Digital (116, 148, 2050)-net over F8, using
- net defined by OOA [i] based on linear OOA(8148, 2050, F8, 32, 32) (dual of [(2050, 32), 65452, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(8148, 32800, F8, 32) (dual of [32800, 32652, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(8148, 32805, F8, 32) (dual of [32805, 32657, 33]-code), using
- construction X applied to Ce(32) ⊂ Ce(25) [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(8111, 32768, F8, 26) (dual of [32768, 32657, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(32) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(8148, 32805, F8, 32) (dual of [32805, 32657, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(8148, 32800, F8, 32) (dual of [32800, 32652, 33]-code), using
(148−32, 148, 36362)-Net over F8 — Digital
Digital (116, 148, 36362)-net over F8, using
(148−32, 148, large)-Net in Base 8 — Upper bound on s
There is no (116, 148, large)-net in base 8, because
- 30 times m-reduction [i] would yield (116, 118, large)-net in base 8, but