Best Known (20, 20+∞, s)-Nets in Base 9
(20, 20+∞, 74)-Net over F9 — Constructive and digital
Digital (20, m, 74)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (20, 73)-sequence over F9, using
- t-expansion [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
- t-expansion [i] based on digital (17, 73)-sequence over F9, using
(20, 20+∞, 84)-Net over F9 — Digital
Digital (20, m, 84)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (20, 83)-sequence over F9, using
- t-expansion [i] based on digital (19, 83)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 19 and N(F) ≥ 84, using
- t-expansion [i] based on digital (19, 83)-sequence over F9, using
(20, 20+∞, 182)-Net in Base 9 — Upper bound on s
There is no (20, m, 183)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (20, 363, 183)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9363, 183, S9, 2, 343), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 325637 210848 374352 210345 728428 959497 177973 347751 372838 925586 534840 922496 226575 856248 144028 150168 065111 801715 382098 122548 271559 638949 204361 642970 218776 894185 697673 507758 049405 017571 152150 862784 074473 901106 128377 379909 825197 424796 159518 080928 949435 452898 726371 244113 369381 442841 085601 246822 693313 570325 635801 102675 084540 669980 410874 425400 263677 693766 / 43 > 9363 [i]
- extracting embedded OOA [i] would yield OOA(9363, 183, S9, 2, 343), but