Best Known (130−14, 130, s)-Nets in Base 16
(130−14, 130, 4858764)-Net over F16 — Constructive and digital
Digital (116, 130, 4858764)-net over F16, using
- 161 times duplication [i] based on digital (115, 129, 4858764)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (8, 12, 65280)-net over F16, using
- net defined by OOA [i] based on linear OOA(1612, 65280, F16, 4, 4) (dual of [(65280, 4), 261108, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(1612, 130560, F16, 4) (dual of [130560, 130548, 5]-code), using
- trace code [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- 1 times truncation [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- trace code [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(1612, 130560, F16, 4) (dual of [130560, 130548, 5]-code), using
- net defined by OOA [i] based on linear OOA(1612, 65280, F16, 4, 4) (dual of [(65280, 4), 261108, 5]-NRT-code), using
- digital (30, 37, 2396742)-net over F16, using
- s-reduction based on digital (30, 37, 2796200)-net over F16, using
- net defined by OOA [i] based on linear OOA(1637, 2796200, F16, 7, 7) (dual of [(2796200, 7), 19573363, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(1637, 8388601, F16, 7) (dual of [8388601, 8388564, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(1637, large, F16, 7) (dual of [large, large−37, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 1612−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(1637, large, F16, 7) (dual of [large, large−37, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(1637, 8388601, F16, 7) (dual of [8388601, 8388564, 8]-code), using
- net defined by OOA [i] based on linear OOA(1637, 2796200, F16, 7, 7) (dual of [(2796200, 7), 19573363, 8]-NRT-code), using
- s-reduction based on digital (30, 37, 2796200)-net over F16, using
- digital (66, 80, 2396742)-net over F16, using
- trace code for nets [i] based on digital (26, 40, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- trace code for nets [i] based on digital (26, 40, 1198371)-net over F256, using
- digital (8, 12, 65280)-net over F16, using
- generalized (u, u+v)-construction [i] based on
(130−14, 130, large)-Net over F16 — Digital
Digital (116, 130, large)-net over F16, using
- 163 times duplication [i] based on digital (113, 127, large)-net over F16, using
- t-expansion [i] based on digital (104, 127, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16127, large, F16, 23) (dual of [large, large−127, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16127, large, F16, 23) (dual of [large, large−127, 24]-code), using
- t-expansion [i] based on digital (104, 127, large)-net over F16, using
(130−14, 130, large)-Net in Base 16 — Upper bound on s
There is no (116, 130, large)-net in base 16, because
- 12 times m-reduction [i] would yield (116, 118, large)-net in base 16, but