Best Known (80, 97, s)-Nets in Base 8
(80, 97, 32793)-Net over F8 — Constructive and digital
Digital (80, 97, 32793)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 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 (68, 85, 32768)-net over F8, using
- net defined by OOA [i] based on linear OOA(885, 32768, F8, 17, 17) (dual of [(32768, 17), 556971, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using
- net defined by OOA [i] based on linear OOA(885, 32768, F8, 17, 17) (dual of [(32768, 17), 556971, 18]-NRT-code), using
- digital (4, 12, 25)-net over F8, using
(80, 97, 290025)-Net over F8 — Digital
Digital (80, 97, 290025)-net over F8, using
(80, 97, large)-Net in Base 8 — Upper bound on s
There is no (80, 97, large)-net in base 8, because
- 15 times m-reduction [i] would yield (80, 82, large)-net in base 8, but