Best Known (152−115, 152, s)-Nets in Base 8
(152−115, 152, 98)-Net over F8 — Constructive and digital
Digital (37, 152, 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
(152−115, 152, 121)-Net over F8 — Digital
Digital (37, 152, 121)-net over F8, using
- net from sequence [i] based on digital (37, 120)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 121, using
(152−115, 152, 742)-Net in Base 8 — Upper bound on s
There is no (37, 152, 743)-net in base 8, because
- 1 times m-reduction [i] would yield (37, 151, 743)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 23397 445436 158974 828606 943920 759848 738828 931629 182355 287566 092906 709724 819316 385620 394449 052582 794072 945336 818792 737523 263506 353775 271888 > 8151 [i]