Best Known (16, 16+85, s)-Nets in Base 8
(16, 16+85, 65)-Net over F8 — Constructive and digital
Digital (16, 101, 65)-net over F8, using
- t-expansion [i] based on digital (14, 101, 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, 16+85, 296)-Net in Base 8 — Upper bound on s
There is no (16, 101, 297)-net in base 8, because
- 5 times m-reduction [i] would yield (16, 96, 297)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(896, 297, S8, 80), but
- 3 times code embedding in larger space [i] would yield OA(899, 300, S8, 80), but
- the linear programming bound shows that M ≥ 40 022782 297201 097311 602941 262477 530632 498192 038288 781932 896691 523049 264290 547860 624776 842999 087195 816298 888011 204240 887140 081531 774898 465203 266872 743452 556746 493855 914382 334875 597887 787058 066017 508307 020173 692596 486953 586558 454721 128058 141158 612365 458813 863833 219168 502226 322157 330626 780281 943776 937845 624668 160000 / 112 144605 450332 517274 433685 902420 477313 163747 717026 580973 286696 256705 488731 971868 945331 837776 320382 971533 050290 015353 442916 916829 634317 569734 549994 680445 127422 212514 399315 987935 944025 585334 872077 862187 874485 729141 000545 651461 > 899 [i]
- 3 times code embedding in larger space [i] would yield OA(899, 300, S8, 80), but
- extracting embedded orthogonal array [i] would yield OA(896, 297, S8, 80), but