Best Known (66, 66+11, s)-Nets in Base 8
(66, 66+11, 1677720)-Net over F8 — Constructive and digital
Digital (66, 77, 1677720)-net over F8, using
- 84 times duplication [i] based on digital (62, 73, 1677720)-net over F8, using
- net defined by OOA [i] based on linear OOA(873, 1677720, F8, 11, 11) (dual of [(1677720, 11), 18454847, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(873, 8388601, F8, 11) (dual of [8388601, 8388528, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(873, large, F8, 11) (dual of [large, large−73, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(873, large, F8, 11) (dual of [large, large−73, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(873, 8388601, F8, 11) (dual of [8388601, 8388528, 12]-code), using
- net defined by OOA [i] based on linear OOA(873, 1677720, F8, 11, 11) (dual of [(1677720, 11), 18454847, 12]-NRT-code), using
(66, 66+11, large)-Net over F8 — Digital
Digital (66, 77, large)-net over F8, using
- 84 times duplication [i] based on digital (62, 73, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(873, large, F8, 11) (dual of [large, large−73, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(873, large, F8, 11) (dual of [large, large−73, 12]-code), using
(66, 66+11, large)-Net in Base 8 — Upper bound on s
There is no (66, 77, large)-net in base 8, because
- 9 times m-reduction [i] would yield (66, 68, large)-net in base 8, but