Best Known (117−20, 117, s)-Nets in Base 16
(117−20, 117, 1677720)-Net over F16 — Constructive and digital
Digital (97, 117, 1677720)-net over F16, using
- 161 times duplication [i] based on digital (96, 116, 1677720)-net over F16, using
- net defined by OOA [i] based on linear OOA(16116, 1677720, F16, 22, 20) (dual of [(1677720, 22), 36909724, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(16116, 8388601, F16, 2, 20) (dual of [(8388601, 2), 16777086, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16116, 8388602, F16, 2, 20) (dual of [(8388602, 2), 16777088, 21]-NRT-code), using
- trace code [i] based on linear OOA(25658, 4194301, F256, 2, 20) (dual of [(4194301, 2), 8388544, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25658, 8388602, F256, 20) (dual of [8388602, 8388544, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- OOA 2-folding [i] based on linear OA(25658, 8388602, F256, 20) (dual of [8388602, 8388544, 21]-code), using
- trace code [i] based on linear OOA(25658, 4194301, F256, 2, 20) (dual of [(4194301, 2), 8388544, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16116, 8388602, F16, 2, 20) (dual of [(8388602, 2), 16777088, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(16116, 8388601, F16, 2, 20) (dual of [(8388601, 2), 16777086, 21]-NRT-code), using
- net defined by OOA [i] based on linear OOA(16116, 1677720, F16, 22, 20) (dual of [(1677720, 22), 36909724, 21]-NRT-code), using
(117−20, 117, large)-Net over F16 — Digital
Digital (97, 117, large)-net over F16, using
- 162 times duplication [i] based on digital (95, 115, large)-net over F16, using
- t-expansion [i] based on digital (94, 115, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16115, large, F16, 21) (dual of [large, large−115, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16115, large, F16, 21) (dual of [large, large−115, 22]-code), using
- t-expansion [i] based on digital (94, 115, large)-net over F16, using
(117−20, 117, large)-Net in Base 16 — Upper bound on s
There is no (97, 117, large)-net in base 16, because
- 18 times m-reduction [i] would yield (97, 99, large)-net in base 16, but