Best Known (117−89, 117, s)-Nets in Base 8
(117−89, 117, 65)-Net over F8 — Constructive and digital
Digital (28, 117, 65)-net over F8, using
- t-expansion [i] based on digital (14, 117, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(117−89, 117, 97)-Net over F8 — Digital
Digital (28, 117, 97)-net over F8, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 28 and N(F) ≥ 97, using
(117−89, 117, 565)-Net in Base 8 — Upper bound on s
There is no (28, 117, 566)-net in base 8, because
- 1 times m-reduction [i] would yield (28, 116, 566)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 612 229552 847252 526842 727594 180792 663527 507378 204770 000329 302033 080206 130342 119556 158149 671853 227355 942030 > 8116 [i]