Best Known (64, 64+17, s)-Nets in Base 8
(64, 64+17, 4113)-Net over F8 — Constructive and digital
Digital (64, 81, 4113)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 10, 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 (54, 71, 4096)-net over F8, using
- net defined by OOA [i] based on linear OOA(871, 4096, F8, 17, 17) (dual of [(4096, 17), 69561, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, 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(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using
- net defined by OOA [i] based on linear OOA(871, 4096, F8, 17, 17) (dual of [(4096, 17), 69561, 18]-NRT-code), using
- digital (2, 10, 17)-net over F8, using
(64, 64+17, 36260)-Net over F8 — Digital
Digital (64, 81, 36260)-net over F8, using
(64, 64+17, large)-Net in Base 8 — Upper bound on s
There is no (64, 81, large)-net in base 8, because
- 15 times m-reduction [i] would yield (64, 66, large)-net in base 8, but