MinT - Best Known (6, 6+∞, s)-Nets in Base 128

Best Known (6, 6+∞, s)-Nets in Base 128

(6, 6+∞, 216)-Net over F₁₂₈ — Constructive and digital

Digital (6, m, 216)-net over F₁₂₈ for arbitrarily large m, using

net from sequence [i] based on digital (6, 215)-sequence over F₁₂₈, using
- t-expansion [i] based on digital (5, 215)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
    - a function field by SÃ©mirat [i]

(6, 6+∞, 243)-Net over F₁₂₈ — Digital

Digital (6, m, 243)-net over F₁₂₈ for arbitrarily large m, using

net from sequence [i] based on digital (6, 242)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 6 and N(F) ≥ 243, using
  - a curve from the manYPoints database [i]

(6, 6+∞, 903)-Net in Base 128 — Upper bound on s

There is no (6, m, 904)-net in base 128 for arbitrarily large m, because

m-reduction [i] would yield (6, 902, 904)-net in base 128, but
- extracting embedded OOA [i] would yield OA(128⁹⁰², 904, S₁₂₈, 896), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 51 724056 688792 338097 715763 368145 087671 250480 301752 880297 867190 150614 220497 749669 288655 417120 494530 720535 924104 073526 762295 433405 682928 616670 205604 843147 058465 169415 847876 741600 110048 504846 585821 024394 097605 408684 869443 793511 305665 387405 326735 411169 690425 819320 976167 634343 093741 239932 227506 315663 315377 050747 594605 691799 258570 700603 191426 635581 581386 321052 666850 503882 627686 445139 657389 090779 170211 897515 345034 489142 735855 913830 063268 220237 079450 744595 192299 742290 372039 829933 333378 980673 496636 339340 070174 326092 802214 859102 354429 162547 193310 894262 694868 356424 526124 774434 506632 830686 782786 888926 537346 535258 724213 064212 865949 622085 405197 228850 550768 082105 051521 529642 201315 330405 992939 391376 139904 126933 171906 083363 124142 989141 035723 984751 010694 436913 901323 814549 505073 633813 425793 976236 758391 135215 188601 394775 381283 309855 031709 371566 712516 471140 566600 741221 677858 341365 531866 950066 927253 823342 713436 816512 435366 355875 974350 067403 967001 576595 091395 735442 143900 861809 184286 119769 524433 246983 043253 335111 236480 844733 270645 947006 083666 936404 083068 690835 404229 782042 766417 890119 530148 670662 213521 347029 940274 804894 994279 702587 566797 916458 283476 488507 447902 934974 179248 178336 945255 827241 872735 560568 123704 282107 138932 530659 308693 049956 017420 909392 777312 655539 057903 320668 432705 653145 888321 853788 160892 149404 728850 011231 388411 349033 488639 348496 919321 897009 491823 517729 730225 140064 571748 903288 078347 448172 210350 764088 097981 460507 213904 169878 298987 865086 619036 229049 987035 988149 847272 806742 086152 397513 078758 838205 273904 239637 862731 461217 922879 473725 009417 997672 086030 746794 655971 975525 272620 180822 927383 113674 010369 797623 333737 865835 593079 577184 464915 507096 728900 067047 350180 752384 031640 710770 784220 364224 927484 957064 809035 117685 955214 363244 600021 484940 078794 896986 434684 397480 074023 058735 597842 373541 802802 666208 934060 575624 779892 878674 902968 420197 538527 163004 060803 687483 389796 397446 008222 009352 800715 145216 / 897 > 128⁹⁰² [i]

Best Known (6, 6+∞, s)-Nets in Base 128

(6, 6+∞, 216)-Net over F128 — Constructive and digital

(6, 6+∞, 243)-Net over F128 — Digital

(6, 6+∞, 903)-Net in Base 128 — Upper bound on s

(6, 6+∞, 216)-Net over F₁₂₈ — Constructive and digital

(6, 6+∞, 243)-Net over F₁₂₈ — Digital