Best Known (7, 7+44, s)-Nets in Base 9
(7, 7+44, 36)-Net over F9 — Constructive and digital
Digital (7, 51, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
(7, 7+44, 40)-Net over F9 — Digital
Digital (7, 51, 40)-net over F9, using
- net from sequence [i] based on digital (7, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 40, using
(7, 7+44, 137)-Net in Base 9 — Upper bound on s
There is no (7, 51, 138)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(951, 138, S9, 44), but
- the linear programming bound shows that M ≥ 838 209185 651930 664186 141941 523946 677561 211005 508496 469814 795774 197619 379123 691624 800030 128907 727232 337205 / 169 475951 936136 771675 464592 182783 546712 823696 327016 208581 > 951 [i]