Best Known (36, 169, s)-Nets in Base 8
(36, 169, 65)-Net over F8 — Constructive and digital
Digital (36, 169, 65)-net over F8, using
- t-expansion [i] based on digital (14, 169, 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
(36, 169, 112)-Net over F8 — Digital
Digital (36, 169, 112)-net over F8, using
- t-expansion [i] based on digital (35, 169, 112)-net over F8, using
- net from sequence [i] based on digital (35, 111)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 35 and N(F) ≥ 112, using
- net from sequence [i] based on digital (35, 111)-sequence over F8, using
(36, 169, 681)-Net in Base 8 — Upper bound on s
There is no (36, 169, 682)-net in base 8, because
- 1 times m-reduction [i] would yield (36, 168, 682)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 56 504552 191282 575993 916528 606586 369169 961677 366366 624868 077554 399340 818150 526344 856459 990411 871621 360941 108182 761900 218140 608772 037123 769878 248615 846440 > 8168 [i]