Best Known (140−103, 140, s)-Nets in Base 8
(140−103, 140, 98)-Net over F8 — Constructive and digital
Digital (37, 140, 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
(140−103, 140, 121)-Net over F8 — Digital
Digital (37, 140, 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
(140−103, 140, 788)-Net in Base 8 — Upper bound on s
There is no (37, 140, 789)-net in base 8, because
- 1 times m-reduction [i] would yield (37, 139, 789)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 345407 422066 533535 048724 326087 598147 035223 612585 543824 547163 570259 571816 976824 983468 947059 522297 119721 394888 202206 602539 016864 > 8139 [i]