Best Known (75−15, 75, s)-Nets in Base 8
(75−15, 75, 4698)-Net over F8 — Constructive and digital
Digital (60, 75, 4698)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 9, 17)-net over F8, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- digital (51, 66, 4681)-net over F8, using
- net defined by OOA [i] based on linear OOA(866, 4681, F8, 15, 15) (dual of [(4681, 15), 70149, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(866, 32768, F8, 15) (dual of [32768, 32702, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(866, 32768, F8, 15) (dual of [32768, 32702, 16]-code), using
- net defined by OOA [i] based on linear OOA(866, 4681, F8, 15, 15) (dual of [(4681, 15), 70149, 16]-NRT-code), using
- digital (2, 9, 17)-net over F8, using
(75−15, 75, 59483)-Net over F8 — Digital
Digital (60, 75, 59483)-net over F8, using
(75−15, 75, large)-Net in Base 8 — Upper bound on s
There is no (60, 75, large)-net in base 8, because
- 13 times m-reduction [i] would yield (60, 62, large)-net in base 8, but