Best Known (20, 20+80, s)-Nets in Base 8
(20, 20+80, 65)-Net over F8 — Constructive and digital
Digital (20, 100, 65)-net over F8, using
- t-expansion [i] based on digital (14, 100, 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
(20, 20+80, 76)-Net over F8 — Digital
Digital (20, 100, 76)-net over F8, using
- net from sequence [i] based on digital (20, 75)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 20 and N(F) ≥ 76, using
(20, 20+80, 383)-Net in Base 8 — Upper bound on s
There is no (20, 100, 384)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 2 242080 626396 625966 521125 535936 124583 761258 018956 957551 248776 464804 529652 646852 282012 770093 > 8100 [i]