Best Known (20, 20+∞, s)-Nets in Base 49
(20, 20+∞, 96)-Net over F49 — Constructive and digital
Digital (20, m, 96)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (20, 95)-sequence over F49, using
- t-expansion [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
- t-expansion [i] based on digital (17, 95)-sequence over F49, using
(20, 20+∞, 1050)-Net in Base 49 — Upper bound on s
There is no (20, m, 1051)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (20, 1049, 1051)-net in base 49, but
- extracting embedded OOA [i] would yield OA(491049, 1051, S49, 1029), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 558826 143024 848675 091123 751815 132385 844158 696270 627473 277512 856793 236890 561803 435409 048238 327414 506227 294620 463253 612604 590844 996495 689799 030647 956182 160599 186291 709896 500872 872540 496463 197331 171291 333612 641219 187473 445245 456751 943641 597561 365546 019851 799686 694494 647018 908155 099528 654271 415668 554188 352239 365516 500337 091235 757467 228584 329117 966493 066499 432659 619522 294527 150595 825509 858771 777764 468638 275246 395377 872084 071942 954313 154820 582390 853870 033034 486397 940490 576279 410391 575030 638498 713015 028809 736559 258801 151954 692248 995829 720747 080911 092819 058092 487327 205466 834312 059852 428186 049033 915632 011976 511437 974926 293607 997942 379383 076599 236346 669507 580407 787734 445064 061394 013710 973214 890014 282988 437582 323998 134090 383684 179653 374506 855954 907089 441095 945666 773482 812477 315777 435975 338545 086282 767575 140505 879846 087428 542114 458665 229222 047678 545529 740568 071398 664086 573525 120531 652838 262425 927893 840609 655615 049461 508926 656532 965560 444008 897024 845872 776002 383678 319803 990825 481149 636950 148730 513466 364058 537015 402042 305973 661743 506309 594399 880063 330606 009721 970633 596474 771438 054120 986955 270837 759003 342899 612926 480718 596428 597109 648158 093693 509975 725196 632915 994449 148660 424623 685722 353030 315422 021310 608499 206246 180915 870357 134860 297043 371096 804306 184513 190474 254396 203616 764177 758603 514232 298633 866368 440666 148980 686201 734081 583571 054043 147547 271454 710643 226406 897885 804062 181227 595634 636352 872667 348847 026493 187399 673452 277182 821270 208441 104164 290630 891247 379198 666119 560082 158009 211357 570698 622699 516819 795059 117511 987043 428412 932917 439523 583865 938411 772475 539204 820929 227459 239929 520659 985213 410925 395799 270246 093224 904797 672471 936772 295793 685218 471814 885471 118730 943760 317368 845470 454187 538779 170258 610201 997573 728832 917871 250070 833091 579273 288064 450746 046381 860011 / 515 > 491049 [i]
- extracting embedded OOA [i] would yield OA(491049, 1051, S49, 1029), but