Best Known (29, 29+144, s)-Nets in Base 8
(29, 29+144, 65)-Net over F8 — Constructive and digital
Digital (29, 173, 65)-net over F8, using
- t-expansion [i] based on digital (14, 173, 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
(29, 29+144, 97)-Net over F8 — Digital
Digital (29, 173, 97)-net over F8, using
- t-expansion [i] based on digital (28, 173, 97)-net over F8, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 28 and N(F) ≥ 97, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
(29, 29+144, 538)-Net in Base 8 — Upper bound on s
There is no (29, 173, 539)-net in base 8, because
- 2 times m-reduction [i] would yield (29, 171, 539)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 27612 665833 549641 006533 351851 416393 268585 620641 291558 469114 614550 962312 020008 963561 232180 218725 078182 170242 890980 487371 179742 729493 583911 971922 580395 024576 > 8171 [i]