MinT - Best Known (12, 12+∞, s)-Nets in Base 25

Best Known (12, 12+∞, s)-Nets in Base 25

Digital (12, m, 126)-net over F₂₅ for arbitrarily large m, using

net from sequence [i] based on digital (12, 125)-sequence over F₂₅, using
- t-expansion [i] based on digital (10, 125)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [i]

There is no (12, m, 338)-net in base 25 for arbitrarily large m, because

m-reduction [i] would yield (12, 673, 338)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(25⁶⁷³, 338, S₂₅, 2, 661), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 30 925693 397737 668480 491272 612287 614067 879594 381336 196132 022286 614890 137616 253029 440135 856725 665245 422572 281333 999113 798141 376155 893458 777517 522774 350402 761061 745451 993780 139117 313413 841472 613484 375951 555466 738512 592211 407024 430044 547024 482807 127729 812005 573532 969958 373231 039763 943338 062324 871700 163807 381004 725926 866435 841666 739844 067176 044356 090287 805378 064726 791171 734667 227858 353718 865767 643821 380692 902414 701399 767706 763264 793364 836107 148406 772294 421694 082750 898350 078254 330163 314733 811639 815691 386836 785007 213107 224400 272528 361580 186766 779689 004169 327889 137139 199403 616035 042584 439731 795597 513196 605944 722446 966490 693733 264126 838564 363929 907562 266668 707582 639058 758854 566040 991237 094983 491268 432863 421746 419863 194877 781897 226550 708120 805653 824986 363951 422471 483323 313457 908064 629764 870742 586068 635309 874597 491295 857221 953045 329003 398023 112716 830468 063763 415191 082009 021078 334881 955272 095764 073836 225704 905444 899850 408546 626567 840576 171875 / 331 > 25⁶⁷³ [i]