Best Known (50, 159, s)-Nets in Base 8
(50, 159, 98)-Net over F8 — Constructive and digital
Digital (50, 159, 98)-net over F8, using
- t-expansion [i] based on digital (37, 159, 98)-net over F8, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
- net from sequence [i] based on digital (37, 97)-sequence over F8, using
(50, 159, 144)-Net over F8 — Digital
Digital (50, 159, 144)-net over F8, using
- t-expansion [i] based on digital (45, 159, 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
(50, 159, 1280)-Net in Base 8 — Upper bound on s
There is no (50, 159, 1281)-net in base 8, because
- 1 times m-reduction [i] would yield (50, 158, 1281)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 49320 206299 682700 160961 307615 169047 621734 582638 133734 544076 662335 936915 399352 207204 678907 946278 717547 881003 568767 539393 382491 606406 783844 471936 > 8158 [i]