Best Known (173−26, 173, s)-Nets in Base 8
(173−26, 173, 161347)-Net over F8 — Constructive and digital
Digital (147, 173, 161347)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 18, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- digital (129, 155, 161319)-net over F8, using
- net defined by OOA [i] based on linear OOA(8155, 161319, F8, 26, 26) (dual of [(161319, 26), 4194139, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(8155, 2097147, F8, 26) (dual of [2097147, 2096992, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(8155, 2097152, F8, 26) (dual of [2097152, 2096997, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(8155, 2097147, F8, 26) (dual of [2097147, 2096992, 27]-code), using
- net defined by OOA [i] based on linear OOA(8155, 161319, F8, 26, 26) (dual of [(161319, 26), 4194139, 27]-NRT-code), using
- digital (5, 18, 28)-net over F8, using
(173−26, 173, 2581740)-Net over F8 — Digital
Digital (147, 173, 2581740)-net over F8, using
(173−26, 173, large)-Net in Base 8 — Upper bound on s
There is no (147, 173, large)-net in base 8, because
- 24 times m-reduction [i] would yield (147, 149, large)-net in base 8, but