Best Known (76, 76+97, s)-Nets in Base 8
(76, 76+97, 130)-Net over F8 — Constructive and digital
Digital (76, 173, 130)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 62, 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 (14, 111, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8 (see above)
- digital (14, 62, 65)-net over F8, using
(76, 76+97, 175)-Net over F8 — Digital
Digital (76, 173, 175)-net over F8, using
(76, 76+97, 4580)-Net in Base 8 — Upper bound on s
There is no (76, 173, 4581)-net in base 8, because
- 1 times m-reduction [i] would yield (76, 172, 4581)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 215925 392283 860684 155137 133685 655902 581460 869627 485326 693866 814963 344810 723260 175436 199139 932846 970182 821746 677825 975213 999253 208653 448809 220213 644513 352196 > 8172 [i]