Best Known (163−24, 163, s)-Nets in Base 8
(163−24, 163, 174787)-Net over F8 — Constructive and digital
Digital (139, 163, 174787)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (4, 16, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- digital (123, 147, 174762)-net over F8, using
- net defined by OOA [i] based on linear OOA(8147, 174762, F8, 24, 24) (dual of [(174762, 24), 4194141, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(8147, 2097144, F8, 24) (dual of [2097144, 2096997, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8147, 2097151, F8, 24) (dual of [2097151, 2097004, 25]-code), using
- 1 times truncation [i] 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]
- 1 times truncation [i] based on linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8147, 2097151, F8, 24) (dual of [2097151, 2097004, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(8147, 2097144, F8, 24) (dual of [2097144, 2096997, 25]-code), using
- net defined by OOA [i] based on linear OOA(8147, 174762, F8, 24, 24) (dual of [(174762, 24), 4194141, 25]-NRT-code), using
- digital (4, 16, 25)-net over F8, using
(163−24, 163, 3384692)-Net over F8 — Digital
Digital (139, 163, 3384692)-net over F8, using
(163−24, 163, large)-Net in Base 8 — Upper bound on s
There is no (139, 163, large)-net in base 8, because
- 22 times m-reduction [i] would yield (139, 141, large)-net in base 8, but