Best Known (89, 89+14, s)-Nets in Base 8
(89, 89+14, 1198371)-Net over F8 — Constructive and digital
Digital (89, 103, 1198371)-net over F8, using
- 86 times duplication [i] based on digital (83, 97, 1198371)-net over F8, using
- net defined by OOA [i] based on linear OOA(897, 1198371, F8, 14, 14) (dual of [(1198371, 14), 16777097, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(897, 8388597, F8, 14) (dual of [8388597, 8388500, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(897, large, F8, 14) (dual of [large, large−97, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(897, large, F8, 14) (dual of [large, large−97, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(897, 8388597, F8, 14) (dual of [8388597, 8388500, 15]-code), using
- net defined by OOA [i] based on linear OOA(897, 1198371, F8, 14, 14) (dual of [(1198371, 14), 16777097, 15]-NRT-code), using
(89, 89+14, large)-Net over F8 — Digital
Digital (89, 103, large)-net over F8, using
- 86 times duplication [i] based on digital (83, 97, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(897, large, F8, 14) (dual of [large, large−97, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(897, large, F8, 14) (dual of [large, large−97, 15]-code), using
(89, 89+14, large)-Net in Base 8 — Upper bound on s
There is no (89, 103, large)-net in base 8, because
- 12 times m-reduction [i] would yield (89, 91, large)-net in base 8, but