Best Known (166−21, 166, s)-Nets in Base 8
(166−21, 166, 1677720)-Net over F8 — Constructive and digital
Digital (145, 166, 1677720)-net over F8, using
- 84 times duplication [i] based on digital (141, 162, 1677720)-net over F8, using
- net defined by OOA [i] based on linear OOA(8162, 1677720, F8, 22, 21) (dual of [(1677720, 22), 36909678, 22]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(8162, 8388601, F8, 2, 21) (dual of [(8388601, 2), 16777040, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8162, 8388602, F8, 2, 21) (dual of [(8388602, 2), 16777042, 22]-NRT-code), using
- trace code [i] based on linear OOA(6481, 4194301, F64, 2, 21) (dual of [(4194301, 2), 8388521, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6481, 8388602, F64, 21) (dual of [8388602, 8388521, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(6481, large, F64, 21) (dual of [large, large−81, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6481, large, F64, 21) (dual of [large, large−81, 22]-code), using
- OOA 2-folding [i] based on linear OA(6481, 8388602, F64, 21) (dual of [8388602, 8388521, 22]-code), using
- trace code [i] based on linear OOA(6481, 4194301, F64, 2, 21) (dual of [(4194301, 2), 8388521, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8162, 8388602, F8, 2, 21) (dual of [(8388602, 2), 16777042, 22]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(8162, 8388601, F8, 2, 21) (dual of [(8388601, 2), 16777040, 22]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8162, 1677720, F8, 22, 21) (dual of [(1677720, 22), 36909678, 22]-NRT-code), using
(166−21, 166, large)-Net over F8 — Digital
Digital (145, 166, large)-net over F8, using
- t-expansion [i] based on digital (144, 166, large)-net over F8, using
- 2 times m-reduction [i] based on digital (144, 168, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8168, large, F8, 24) (dual of [large, large−168, 25]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8168, large, F8, 24) (dual of [large, large−168, 25]-code), using
- 2 times m-reduction [i] based on digital (144, 168, large)-net over F8, using
(166−21, 166, large)-Net in Base 8 — Upper bound on s
There is no (145, 166, large)-net in base 8, because
- 19 times m-reduction [i] would yield (145, 147, large)-net in base 8, but