Best Known (17, ∞, s)-Nets in Base 49
(17, ∞, 96)-Net over F49 — Constructive and digital
Digital (17, m, 96)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (17, 95)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) ≤ 17 and N(F) ≥ 96, using
- F4 from the tower of function fields by GarcÃa, Stichtenoth, and Rück over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) ≤ 17 and N(F) ≥ 96, using
(17, ∞, 900)-Net in Base 49 — Upper bound on s
There is no (17, m, 901)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (17, 899, 901)-net in base 49, but
- extracting embedded OOA [i] would yield OA(49899, 901, S49, 882), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 28524 998261 080822 402272 259306 174834 098431 434850 167302 022615 467307 237762 595234 854282 446666 114518 067488 725036 133140 449091 616292 082345 277455 779435 673170 389028 267419 866046 515897 977541 948968 111531 652884 195977 387833 461050 800215 670126 691086 746559 603890 721685 738650 258046 554168 875037 680637 359118 641683 765755 864355 341806 334011 176687 463452 598907 031446 571704 903605 438745 106623 654601 035073 497656 714699 621159 082629 361708 094628 942283 587229 912128 099471 428349 097019 054112 923896 767840 360981 599724 705207 935415 840618 681525 115333 775811 427845 732284 600489 086184 930035 321264 627567 445399 327586 205226 253113 668778 053615 141723 029734 631720 701685 266905 572310 472911 850743 346060 584831 249811 726095 396893 038417 679137 863868 823232 331149 467478 311145 989267 877537 114001 068268 807565 990091 299959 684158 732045 668661 643802 025724 456456 719514 913177 501033 681071 917960 963765 264475 578044 410162 559669 743639 207708 979060 114362 544868 098172 069370 270454 979898 684629 875981 318981 728731 902060 743224 088470 510703 772767 224048 544525 279166 579224 265014 719377 604354 955108 591518 706921 024967 106075 464387 713925 577158 712066 244432 606082 283232 748670 612760 394208 265234 324771 177779 940585 744336 701148 547532 153893 825821 039147 406628 974728 529112 367984 391598 052276 302075 163416 061561 230599 501631 822758 521484 428218 514791 713127 378054 680549 608601 213236 201499 280156 332455 886162 457261 810047 541609 032789 559341 832604 430139 801047 680826 875340 196903 886102 695820 924872 173840 955676 156761 029977 485734 318992 889169 073409 495939 742177 343345 266686 488328 006357 989293 568298 755419 701200 462124 156379 757091 717521 814596 520019 / 883 > 49899 [i]
- extracting embedded OOA [i] would yield OA(49899, 901, S49, 882), but