Best Known (45, 45+10, s)-Nets in Base 16
(45, 45+10, 1677720)-Net over F16 — Constructive and digital
Digital (45, 55, 1677720)-net over F16, using
- net defined by OOA [i] based on linear OOA(1655, 1677720, F16, 10, 10) (dual of [(1677720, 10), 16777145, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(1655, 8388600, F16, 10) (dual of [8388600, 8388545, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(1655, large, F16, 10) (dual of [large, large−55, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(1655, large, F16, 10) (dual of [large, large−55, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(1655, 8388600, F16, 10) (dual of [8388600, 8388545, 11]-code), using
(45, 45+10, large)-Net over F16 — Digital
Digital (45, 55, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(1655, large, F16, 10) (dual of [large, large−55, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
(45, 45+10, large)-Net in Base 16 — Upper bound on s
There is no (45, 55, large)-net in base 16, because
- 8 times m-reduction [i] would yield (45, 47, large)-net in base 16, but