Best Known (17, ∞, s)-Nets in Base 9
(17, ∞, 74)-Net over F9 — Constructive and digital
Digital (17, m, 74)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
(17, ∞, 157)-Net in Base 9 — Upper bound on s
There is no (17, m, 158)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (17, 313, 158)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9313, 158, S9, 2, 296), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 650980 615352 716996 772295 805765 732796 112802 815755 482245 796837 968573 210155 105515 404054 676128 440226 662183 571716 895705 412568 258682 063297 508086 048562 913737 743579 733263 788351 165441 240521 395807 872154 689282 949910 662691 517815 989745 049178 802090 967565 494571 387719 288776 025501 521106 413912 631181 358479 352653 503163 / 11 > 9313 [i]
- extracting embedded OOA [i] would yield OOA(9313, 158, S9, 2, 296), but