Best Known (115−63, 115, s)-Nets in Base 8
(115−63, 115, 99)-Net over F8 — Constructive and digital
Digital (52, 115, 99)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 38, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (14, 77, 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
- digital (7, 38, 34)-net over F8, using
(115−63, 115, 144)-Net over F8 — Digital
Digital (52, 115, 144)-net over F8, using
- t-expansion [i] based on digital (45, 115, 144)-net over F8, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 45 and N(F) ≥ 144, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
(115−63, 115, 3695)-Net in Base 8 — Upper bound on s
There is no (52, 115, 3696)-net in base 8, because
- 1 times m-reduction [i] would yield (52, 114, 3696)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 8 978030 468647 724653 017388 801689 046224 880818 457956 128096 662872 098238 037230 971443 248260 795541 248668 464066 > 8114 [i]