Best Known (17, 17+6, s)-Nets in Base 64
(17, 17+6, 2796201)-Net over F64 — Constructive and digital
Digital (17, 23, 2796201)-net over F64, using
- 642 times duplication [i] based on digital (15, 21, 2796201)-net over F64, using
- net defined by OOA [i] based on linear OOA(6421, 2796201, F64, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- net defined by OOA [i] based on linear OOA(6421, 2796201, F64, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
(17, 17+6, large)-Net over F64 — Digital
Digital (17, 23, large)-net over F64, using
- 642 times duplication [i] based on digital (15, 21, large)-net over F64, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
(17, 17+6, large)-Net in Base 64 — Upper bound on s
There is no (17, 23, large)-net in base 64, because
- 4 times m-reduction [i] would yield (17, 19, large)-net in base 64, but