MinT - Best Known (17, ∞, s)-Nets in Base 16

Best Known (17, ∞, s)-Nets in Base 16

Digital (17, m, 65)-net over F₁₆ for arbitrarily large m, using

net from sequence [i] based on digital (17, 64)-sequence over F₁₆, using
- t-expansion [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

Digital (17, m, 112)-net over F₁₆ for arbitrarily large m, using

There is no (17, m, 289)-net in base 16 for arbitrarily large m, because

m-reduction [i] would yield (17, 575, 289)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(16⁵⁷⁵, 289, S₁₆, 2, 558), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 183360 628893 714538 186031 988903 377800 502070 512352 851217 598015 663742 024036 469477 868107 928298 057052 521704 458365 074146 047712 128283 351587 930569 177074 678895 497342 466213 432571 717217 148170 102600 207134 918609 677753 995807 421097 934734 971789 786871 960462 927318 504230 174697 210837 673898 428484 403682 599228 461498 052808 533897 124430 088489 181742 742304 327825 266353 660021 648005 305904 421994 652329 928941 586693 438351 337541 278512 681540 326462 617795 089950 439598 563194 488830 635831 226909 717675 616317 343247 608146 145354 186601 547885 516338 173230 744861 884836 543796 903465 409964 396979 802437 705470 281531 578359 561604 337969 980767 973859 935286 319476 129981 746970 526636 366865 635593 263501 785529 204962 735966 418577 477117 100517 394294 348168 822784 / 559 > 16⁵⁷⁵ [i]