Best Known (16, 107, s)-Nets in Base 8
(16, 107, 65)-Net over F8 — Constructive and digital
Digital (16, 107, 65)-net over F8, using
- t-expansion [i] based on digital (14, 107, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(16, 107, 235)-Net over F8 — Upper bound on s (digital)
There is no digital (16, 107, 236)-net over F8, because
- extracting embedded orthogonal array [i] would yield linear OA(8107, 236, F8, 91) (dual of [236, 129, 92]-code), but
- construction Y1 [i] would yield
- OA(8106, 126, S8, 91), but
- the linear programming bound shows that M ≥ 293 187232 858468 601478 195121 704673 897819 671593 603287 520903 422450 275883 600667 509529 168717 037019 908153 862692 395005 509632 / 543 414185 869329 742359 > 8106 [i]
- linear OA(8129, 236, F8, 110) (dual of [236, 107, 111]-code), but
- discarding factors / shortening the dual code would yield linear OA(8129, 230, F8, 110) (dual of [230, 101, 111]-code), but
- construction Y1 [i] would yield
- OA(8128, 144, S8, 110), but
- the linear programming bound shows that M ≥ 6109 893966 434273 613815 828543 318095 703793 603744 881950 919851 825987 742070 359262 466307 770153 217353 472069 496822 008994 926770 763501 404160 / 124 535855 141787 > 8128 [i]
- OA(8101, 230, S8, 86), but
- discarding factors would yield OA(8101, 146, S8, 86), but
- the linear programming bound shows that M ≥ 47452 756982 762840 644180 785646 906838 805374 098587 752364 011747 551574 239635 502216 492748 447610 784265 998302 557863 887131 929643 838881 370395 949171 355783 528448 / 2798 356661 117080 828757 255676 140575 034437 993397 485091 746485 > 8101 [i]
- discarding factors would yield OA(8101, 146, S8, 86), but
- OA(8128, 144, S8, 110), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(8129, 230, F8, 110) (dual of [230, 101, 111]-code), but
- OA(8106, 126, S8, 91), but
- construction Y1 [i] would yield
(16, 107, 295)-Net in Base 8 — Upper bound on s
There is no (16, 107, 296)-net in base 8, because
- 5 times m-reduction [i] would yield (16, 102, 296)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8102, 296, S8, 86), but
- 4 times code embedding in larger space [i] would yield OA(8106, 300, S8, 86), but
- the linear programming bound shows that M ≥ 1 813677 875369 152272 942573 621196 635803 751018 569122 832333 904547 616932 539570 207271 570162 414270 186689 351457 296081 136706 550412 470642 195703 863438 843196 001370 665838 185358 641792 018172 364679 217484 628335 048624 343807 042717 307486 862460 898668 811055 605083 015058 362771 936907 178369 827768 336619 556421 972934 712366 195270 776938 420836 098170 782223 082681 191215 701147 981866 592385 175258 023020 676383 298813 952000 / 2 609523 090828 280360 399673 517605 921202 027302 398919 728637 474815 813018 035055 667380 402821 337345 325099 601925 819413 791707 710882 570618 298161 573338 933318 342533 235415 899785 945735 478446 574545 152392 020552 468875 081370 574983 328005 680478 033720 175186 826334 000457 530734 946272 661810 404405 406720 334371 309973 > 8106 [i]
- 4 times code embedding in larger space [i] would yield OA(8106, 300, S8, 86), but
- extracting embedded orthogonal array [i] would yield OA(8102, 296, S8, 86), but