Best Known (100, 100+12, s)-Nets in Base 5
(100, 100+12, 2796200)-Net over F5 — Constructive and digital
Digital (100, 112, 2796200)-net over F5, using
- net defined by OOA [i] based on linear OOA(5112, 2796200, F5, 14, 12) (dual of [(2796200, 14), 39146688, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(5112, 8388601, F5, 2, 12) (dual of [(8388601, 2), 16777090, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5112, 8388602, F5, 2, 12) (dual of [(8388602, 2), 16777092, 13]-NRT-code), using
- trace code [i] based on linear OOA(2556, 4194301, F25, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2556, 8388602, F25, 12) (dual of [8388602, 8388546, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- OOA 2-folding [i] based on linear OA(2556, 8388602, F25, 12) (dual of [8388602, 8388546, 13]-code), using
- trace code [i] based on linear OOA(2556, 4194301, F25, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5112, 8388602, F5, 2, 12) (dual of [(8388602, 2), 16777092, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(5112, 8388601, F5, 2, 12) (dual of [(8388601, 2), 16777090, 13]-NRT-code), using
(100, 100+12, large)-Net over F5 — Digital
Digital (100, 112, large)-net over F5, using
- 53 times duplication [i] based on digital (97, 109, large)-net over F5, using
- t-expansion [i] based on digital (96, 109, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5109, large, F5, 13) (dual of [large, large−109, 14]-code), using
- 8 times code embedding in larger space [i] based on linear OA(5101, large, F5, 13) (dual of [large, large−101, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 520−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- 8 times code embedding in larger space [i] based on linear OA(5101, large, F5, 13) (dual of [large, large−101, 14]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5109, large, F5, 13) (dual of [large, large−109, 14]-code), using
- t-expansion [i] based on digital (96, 109, large)-net over F5, using
(100, 100+12, large)-Net in Base 5 — Upper bound on s
There is no (100, 112, large)-net in base 5, because
- 10 times m-reduction [i] would yield (100, 102, large)-net in base 5, but