Best Known (99, 99+15, s)-Nets in Base 8
(99, 99+15, 2396742)-Net over F8 — Constructive and digital
Digital (99, 114, 2396742)-net over F8, using
- trace code for nets [i] based on digital (42, 57, 1198371)-net over F64, using
- net defined by OOA [i] based on linear OOA(6457, 1198371, F64, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6457, 8388598, F64, 15) (dual of [8388598, 8388541, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6457, 8388598, F64, 15) (dual of [8388598, 8388541, 16]-code), using
- net defined by OOA [i] based on linear OOA(6457, 1198371, F64, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
(99, 99+15, large)-Net over F8 — Digital
Digital (99, 114, large)-net over F8, using
- 82 times duplication [i] based on digital (97, 112, large)-net over F8, using
- t-expansion [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
- t-expansion [i] based on digital (96, 112, large)-net over F8, using
(99, 99+15, large)-Net in Base 8 — Upper bound on s
There is no (99, 114, large)-net in base 8, because
- 13 times m-reduction [i] would yield (99, 101, large)-net in base 8, but