Best Known (18, 18+∞, s)-Nets in Base 64
(18, 18+∞, 177)-Net over F64 — Constructive and digital
Digital (18, m, 177)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (18, 176)-sequence over F64, using
- t-expansion [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- t-expansion [i] based on digital (7, 176)-sequence over F64, using
(18, 18+∞, 281)-Net over F64 — Digital
Digital (18, m, 281)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (18, 280)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 18 and N(F) ≥ 281, using
(18, 18+∞, 1235)-Net in Base 64 — Upper bound on s
There is no (18, m, 1236)-net in base 64 for arbitrarily large m, because
- m-reduction [i] would yield (18, 1234, 1236)-net in base 64, but
- extracting embedded OOA [i] would yield OA(641234, 1236, S64, 1216), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 857625 855918 624024 563523 670018 146212 973653 566552 631758 519835 098111 082166 401055 619509 133770 279066 854198 141336 052287 979076 483325 090903 367479 810120 097617 973861 421557 866537 369619 103822 412412 710026 983433 948233 203413 037563 495518 675480 246497 834425 306785 768170 099600 022769 027281 359106 615573 331493 741658 916602 610427 373342 130853 802387 706266 210000 842931 685111 845436 990270 990953 577305 117061 917674 242308 413803 974457 457324 580737 076731 533157 116522 523737 002154 980570 657599 154820 024438 324950 207950 686166 639606 048150 936795 317334 897898 770843 569488 434745 674159 017862 979228 732415 932563 418248 129893 077957 060539 107545 191883 723150 891706 208186 339962 759806 080357 926031 665123 082939 849950 544682 007563 452980 224472 682822 048850 785688 610377 097812 922943 688866 403481 978584 283172 550080 303370 252002 253070 379489 376580 771652 483868 372099 423704 876627 378793 137650 210250 998397 458263 587748 115934 575995 627789 804499 863576 847318 108035 686590 434331 565364 311996 414131 824847 536859 344619 864828 897393 648672 448619 968737 381700 964703 191486 710441 811118 817830 314037 511890 490702 086172 737087 936175 484113 003078 771119 375865 975141 470846 403970 896235 480880 129486 346848 526576 526230 901983 307441 099711 609523 366774 280520 853254 547721 060303 761299 482008 902463 948248 053330 552205 402558 930730 101529 995882 261645 427196 206457 362334 788026 449313 782014 639765 900430 738560 650694 170970 937731 914153 825732 211311 485266 428009 835160 160071 215401 080769 164282 392017 478610 346757 988186 732243 907504 517007 809391 246986 159433 978173 009676 053205 295413 498679 942583 436319 082598 155280 575138 192859 928745 549108 500805 937064 048570 376155 969345 560480 025887 943972 531581 831748 007868 039361 524280 591786 492309 567800 452680 414653 861575 758949 106711 146499 222627 243107 816454 715244 874234 555647 534572 727241 830339 023041 946577 766620 876564 141596 395479 138056 234216 271709 414395 219691 040287 355167 531425 902630 253139 746777 769815 788144 141757 209818 929064 278839 342602 412904 712226 347990 639808 723270 476728 125104 074474 132430 569454 623544 904903 625256 236194 576312 057093 233761 950208 226486 216385 938670 641550 935602 347696 550710 529503 005373 031087 527101 496293 113165 211801 474460 274472 226982 265055 799152 964317 629927 671445 165444 310376 349679 739448 056216 222572 931985 521346 263088 403371 249244 215442 951157 276364 221895 095974 637334 454142 925115 657346 542637 019694 119729 119518 601489 940480 / 1217 > 641234 [i]
- extracting embedded OOA [i] would yield OA(641234, 1236, S64, 1216), but