Best Known (75, 75+∞, s)-Nets in Base 9
(75, 75+∞, 165)-Net over F9 — Constructive and digital
Digital (75, m, 165)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (75, 164)-sequence over F9, using
- t-expansion [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- t-expansion [i] based on digital (64, 164)-sequence over F9, using
(75, 75+∞, 192)-Net over F9 — Digital
Digital (75, m, 192)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (75, 191)-sequence over F9, using
- t-expansion [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
- t-expansion [i] based on digital (61, 191)-sequence over F9, using
(75, 75+∞, 627)-Net in Base 9 — Upper bound on s
There is no (75, m, 628)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (75, 1880, 628)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91880, 628, S9, 3, 1805), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 405 858866 496974 095632 217330 706133 875488 658656 051794 028907 893166 360684 383398 409316 383784 419086 099007 701843 339403 685043 142034 097923 270485 065234 071081 082212 706514 115817 831775 308039 659394 786817 772939 285593 818930 221568 826017 553849 766233 525375 748563 567530 233359 089369 266574 437036 145520 257512 166167 567785 299061 877652 589718 620968 496483 844993 202563 900863 982083 165079 406282 464791 450305 939247 625100 119796 244886 837298 982312 643090 670077 604381 293790 354271 980505 589372 911862 192298 114995 174644 074761 278782 721978 515200 238235 113873 524263 792249 878346 602757 721785 401555 735835 393679 107922 085739 521282 327443 710856 006766 416190 032247 737341 940262 502609 938510 255589 951164 115579 410259 277183 325132 449201 025355 432385 948585 335698 278715 393872 744462 415598 803059 883364 869164 183788 593129 518075 119007 277080 350541 539104 852989 071647 229888 682440 028629 650661 450602 236539 431410 956384 383508 151873 808466 921605 816540 906201 682659 400081 090021 367329 626328 995747 214502 079039 671407 735235 926485 683133 972379 000335 283955 230378 264493 904538 919967 265347 008005 833618 411279 723760 441989 330541 305932 909127 957139 573603 481441 548374 672120 617784 059396 271270 905204 303892 402352 546735 498202 848613 654930 449493 904519 550894 793261 465103 288720 185032 182566 627833 023057 186124 508492 622723 701074 386144 680797 008667 891150 062057 281664 641013 197358 203600 458021 859927 946759 637254 021063 294092 029140 027495 102783 143370 359160 663033 085858 726140 392051 425004 644045 592509 058467 931349 783150 237096 225788 024043 566941 572964 713395 071533 564511 556137 926449 568452 615902 654205 779458 859235 981388 022587 970607 069444 589029 328528 553815 349682 826064 542128 721400 661888 768429 836201 305551 620707 355767 849038 888929 760096 793805 207953 243631 033665 000156 105597 094282 018193 575395 267343 356549 577997 931378 633706 420608 874560 877809 109307 865867 832290 999575 045470 794617 326318 577967 852218 548081 385133 028187 330823 749229 / 301 > 91880 [i]
- extracting embedded OOA [i] would yield OOA(91880, 628, S9, 3, 1805), but