Best Known (26, 26+85, s)-Nets in Base 8
(26, 26+85, 65)-Net over F8 — Constructive and digital
Digital (26, 111, 65)-net over F8, using
- t-expansion [i] based on digital (14, 111, 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
(26, 26+85, 86)-Net over F8 — Digital
Digital (26, 111, 86)-net over F8, using
- t-expansion [i] based on digital (25, 111, 86)-net over F8, using
- net from sequence [i] based on digital (25, 85)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 25 and N(F) ≥ 86, using
- net from sequence [i] based on digital (25, 85)-sequence over F8, using
(26, 26+85, 520)-Net in Base 8 — Upper bound on s
There is no (26, 111, 521)-net in base 8, because
- 1 times m-reduction [i] would yield (26, 110, 521)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 2217 135963 445452 031724 210847 713331 580132 710536 851381 407057 502723 525870 495208 685710 757099 341904 728832 > 8110 [i]