Best Known (16, 16+104, s)-Nets in Base 9
(16, 16+104, 64)-Net over F9 — Constructive and digital
Digital (16, 120, 64)-net over F9, using
- t-expansion [i] based on digital (13, 120, 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
(16, 16+104, 74)-Net over F9 — Digital
Digital (16, 120, 74)-net over F9, using
- net from sequence [i] based on digital (16, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 16 and N(F) ≥ 74, using
(16, 16+104, 253)-Net over F9 — Upper bound on s (digital)
There is no digital (16, 120, 254)-net over F9, because
- extracting embedded orthogonal array [i] would yield linear OA(9120, 254, F9, 104) (dual of [254, 134, 105]-code), but
- construction Y1 [i] would yield
- OA(9119, 137, S9, 104), but
- the linear programming bound shows that M ≥ 1 649743 959172 993378 210906 967412 042627 075594 345401 873516 549288 005769 316925 057707 239007 022709 124331 368314 618099 062045 429872 721572 150117 / 4 003686 893566 937500 > 9119 [i]
- linear OA(9134, 254, F9, 117) (dual of [254, 120, 118]-code), but
- discarding factors / shortening the dual code would yield linear OA(9134, 251, F9, 117) (dual of [251, 117, 118]-code), but
- residual code [i] would yield OA(917, 133, S9, 13), but
- 1 times truncation [i] would yield OA(916, 132, S9, 12), but
- the linear programming bound shows that M ≥ 366759 481988 110308 514537 173543 / 191 274702 307783 > 916 [i]
- 1 times truncation [i] would yield OA(916, 132, S9, 12), but
- residual code [i] would yield OA(917, 133, S9, 13), but
- discarding factors / shortening the dual code would yield linear OA(9134, 251, F9, 117) (dual of [251, 117, 118]-code), but
- OA(9119, 137, S9, 104), but
- construction Y1 [i] would yield
(16, 16+104, 296)-Net in Base 9 — Upper bound on s
There is no (16, 120, 297)-net in base 9, because
- 6 times m-reduction [i] would yield (16, 114, 297)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9114, 297, S9, 98), but
- 3 times code embedding in larger space [i] would yield OA(9117, 300, S9, 98), but
- the linear programming bound shows that M ≥ 368978 185014 481871 758974 828757 909993 693993 847343 888158 912567 348091 020643 834977 540265 425632 843896 070601 187041 151291 832424 334247 294034 935799 840440 477271 578399 850979 508583 295243 384166 546991 115076 374588 818620 377334 927239 103863 505500 528461 671536 608986 356917 168284 677223 042024 683442 323661 324147 437856 116096 108789 187089 458631 324932 530182 740932 905900 665207 263958 723950 078071 692790 394286 632571 408311 673049 584295 581112 271435 346052 / 64 908162 979550 890841 359041 957850 676789 384078 925148 975890 090587 329229 035200 188456 626805 372184 169777 382883 400479 070855 074003 221252 557611 572516 944976 034107 519917 973857 890112 630346 548058 455745 258418 709656 036541 864527 634944 796204 084805 777540 422956 241118 575433 600680 165907 617795 661462 542005 256382 271151 614182 245321 > 9117 [i]
- 3 times code embedding in larger space [i] would yield OA(9117, 300, S9, 98), but
- extracting embedded orthogonal array [i] would yield OA(9114, 297, S9, 98), but