Best Known (110−73, 110, s)-Nets in Base 8
(110−73, 110, 98)-Net over F8 — Constructive and digital
Digital (37, 110, 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
(110−73, 110, 121)-Net over F8 — Digital
Digital (37, 110, 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
(110−73, 110, 1084)-Net in Base 8 — Upper bound on s
There is no (37, 110, 1085)-net in base 8, because
- 1 times m-reduction [i] would yield (37, 109, 1085)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 281 451472 630998 446132 226210 416146 994734 960176 739163 691386 950632 313194 991052 567604 024895 024725 931209 > 8109 [i]