Best Known (113−16, 113, s)-Nets in Base 8
(113−16, 113, 1048575)-Net over F8 — Constructive and digital
Digital (97, 113, 1048575)-net over F8, using
- t-expansion [i] based on digital (96, 113, 1048575)-net over F8, using
- net defined by OOA [i] based on linear OOA(8113, 1048575, F8, 17, 17) (dual of [(1048575, 17), 17825662, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(8113, 8388601, F8, 17) (dual of [8388601, 8388488, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(8113, large, F8, 17) (dual of [large, large−113, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8113, large, F8, 17) (dual of [large, large−113, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(8113, 8388601, F8, 17) (dual of [8388601, 8388488, 18]-code), using
- net defined by OOA [i] based on linear OOA(8113, 1048575, F8, 17, 17) (dual of [(1048575, 17), 17825662, 18]-NRT-code), using
(113−16, 113, large)-Net over F8 — Digital
Digital (97, 113, large)-net over F8, using
- 81 times duplication [i] based on digital (96, 112, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8112, large, F8, 16) (dual of [large, large−112, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8112, large, F8, 16) (dual of [large, large−112, 17]-code), using
(113−16, 113, large)-Net in Base 8 — Upper bound on s
There is no (97, 113, large)-net in base 8, because
- 14 times m-reduction [i] would yield (97, 99, large)-net in base 8, but