Best Known (113−20, 113, s)-Nets in Base 16
(113−20, 113, 838860)-Net over F16 — Constructive and digital
Digital (93, 113, 838860)-net over F16, using
- 164 times duplication [i] based on digital (89, 109, 838860)-net over F16, using
- net defined by OOA [i] based on linear OOA(16109, 838860, F16, 20, 20) (dual of [(838860, 20), 16777091, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(16109, 8388600, F16, 20) (dual of [8388600, 8388491, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(16109, large, F16, 20) (dual of [large, large−109, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(16109, large, F16, 20) (dual of [large, large−109, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(16109, 8388600, F16, 20) (dual of [8388600, 8388491, 21]-code), using
- net defined by OOA [i] based on linear OOA(16109, 838860, F16, 20, 20) (dual of [(838860, 20), 16777091, 21]-NRT-code), using
(113−20, 113, large)-Net over F16 — Digital
Digital (93, 113, large)-net over F16, using
- 164 times duplication [i] based on digital (89, 109, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16109, large, F16, 20) (dual of [large, large−109, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16109, large, F16, 20) (dual of [large, large−109, 21]-code), using
(113−20, 113, large)-Net in Base 16 — Upper bound on s
There is no (93, 113, large)-net in base 16, because
- 18 times m-reduction [i] would yield (93, 95, large)-net in base 16, but