Best Known (225, ∞, s)-Nets in Base 3
(225, ∞, 112)-Net over F3 — Constructive and digital
Digital (225, m, 112)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (225, 111)-sequence over F3, using
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on function field F4/F3 with g(F4) = 79, N(F4) ≥ 2, and N(F4) + N2(F4) ≥ 112 from GarcÃa–Stichtenoth tower as constant field extension [i]
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
(225, ∞, 163)-Net over F3 — Digital
Digital (225, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (225, 162)-sequence over F3, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 151 and N(F) ≥ 163, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
(225, ∞, 464)-Net in Base 3 — Upper bound on s
There is no (225, m, 465)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (225, 2783, 465)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32783, 465, S3, 6, 2558), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 58003 611664 789040 674734 058206 401306 947079 783741 310456 388200 421624 551578 918422 720809 252362 631327 960527 621310 808661 292250 133249 203725 854192 808928 549160 517918 010888 312744 398230 286613 452739 173565 094004 282316 256226 608520 894646 962829 068622 465487 634997 295639 617738 043036 071795 667173 497056 958513 120139 184351 797726 250236 222857 509880 680837 331292 386133 072181 142616 013978 369603 839825 139112 769753 619395 552817 797271 866661 075175 075667 515564 754663 642461 387084 269995 098412 806649 580805 508103 237974 115889 540735 088207 743849 852817 275990 050921 376690 315492 817103 108648 850384 810507 080547 089074 402875 969150 547780 287286 500067 908593 214286 237090 301296 958915 534081 591457 751983 735080 415589 126392 415525 512674 370052 289728 672072 409966 360133 576533 254050 086970 745358 457036 869621 622683 571787 207281 362786 991203 738974 369121 752352 755327 059796 812475 271396 342723 490617 056607 215254 582098 879833 938215 806867 550579 278304 305394 509005 083640 959001 300700 135734 263748 991712 287171 782240 701786 057257 437838 149025 517071 862789 845164 951197 122135 283839 309877 991062 929759 657449 900608 872540 026529 516114 259734 878243 449794 818323 971556 379297 362579 017303 612801 872166 619179 219600 194767 668332 058605 653530 949854 415825 623405 521046 399527 054438 603800 958482 011471 262459 239639 834238 826943 039388 469385 332708 754797 982873 828466 819076 830815 389770 575588 129785 764077 996138 378176 442866 117192 676633 853370 348447 / 853 > 32783 [i]
- extracting embedded OOA [i] would yield OOA(32783, 465, S3, 6, 2558), but