Best Known (168−25, 168, s)-Nets in Base 8
(168−25, 168, 174797)-Net over F8 — Constructive and digital
Digital (143, 168, 174797)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 20, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- digital (123, 148, 174762)-net over F8, using
- net defined by OOA [i] based on linear OOA(8148, 174762, F8, 25, 25) (dual of [(174762, 25), 4368902, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8148, 2097145, F8, 25) (dual of [2097145, 2096997, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8148, 2097145, F8, 25) (dual of [2097145, 2096997, 26]-code), using
- net defined by OOA [i] based on linear OOA(8148, 174762, F8, 25, 25) (dual of [(174762, 25), 4368902, 26]-NRT-code), using
- digital (8, 20, 35)-net over F8, using
(168−25, 168, 174800)-Net in Base 8 — Constructive
(143, 168, 174800)-net in base 8, using
- (u, u+v)-construction [i] based on
- (8, 20, 38)-net in base 8, using
- base change [i] based on digital (3, 15, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- base change [i] based on digital (3, 15, 38)-net over F16, using
- digital (123, 148, 174762)-net over F8, using
- net defined by OOA [i] based on linear OOA(8148, 174762, F8, 25, 25) (dual of [(174762, 25), 4368902, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8148, 2097145, F8, 25) (dual of [2097145, 2096997, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8148, 2097145, F8, 25) (dual of [2097145, 2096997, 26]-code), using
- net defined by OOA [i] based on linear OOA(8148, 174762, F8, 25, 25) (dual of [(174762, 25), 4368902, 26]-NRT-code), using
- (8, 20, 38)-net in base 8, using
(168−25, 168, 2936949)-Net over F8 — Digital
Digital (143, 168, 2936949)-net over F8, using
(168−25, 168, large)-Net in Base 8 — Upper bound on s
There is no (143, 168, large)-net in base 8, because
- 23 times m-reduction [i] would yield (143, 145, large)-net in base 8, but