Best Known (78−64, 78, s)-Nets in Base 9
(78−64, 78, 64)-Net over F9 — Constructive and digital
Digital (14, 78, 64)-net over F9, using
- t-expansion [i] based on digital (13, 78, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
(78−64, 78, 299)-Net in Base 9 — Upper bound on s
There is no (14, 78, 300)-net in base 9, because
- 5 times m-reduction [i] would yield (14, 73, 300)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(973, 300, S9, 59), but
- the linear programming bound shows that M ≥ 1 614101 122438 959728 032296 527149 036613 313308 091685 900917 564175 128363 509302 839919 698145 931112 844353 107270 413137 301739 823669 900419 290955 676179 838258 478042 347288 383560 325865 / 318 549167 038685 476261 913473 617729 234340 696246 391414 497686 399246 827710 136381 692237 275059 607150 040103 > 973 [i]
- extracting embedded orthogonal array [i] would yield OA(973, 300, S9, 59), but