Best Known (9, 9+76, s)-Nets in Base 32
(9, 9+76, 104)-Net over F32 — Constructive and digital
Digital (9, 85, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
(9, 9+76, 108)-Net over F32 — Digital
Digital (9, 85, 108)-net over F32, using
- net from sequence [i] based on digital (9, 107)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 108, using
(9, 9+76, 1099)-Net over F32 — Upper bound on s (digital)
There is no digital (9, 85, 1100)-net over F32, because
- 2 times m-reduction [i] would yield digital (9, 83, 1100)-net over F32, but
- extracting embedded orthogonal array [i] would yield linear OA(3283, 1100, F32, 74) (dual of [1100, 1017, 75]-code), but
- the Johnson bound shows that N ≤ 5 387863 093815 789105 275446 580168 927905 538150 865129 592260 461555 028746 202490 958597 068106 592617 299121 277240 288655 933453 549853 660164 134515 900215 568068 678773 370289 025440 478845 951419 161831 319241 912678 131678 803080 114044 187271 599546 584437 364643 780334 816481 726402 667503 590910 423797 546895 979875 326147 036300 822761 644364 928288 637753 415451 751270 298687 115097 423718 911707 518119 587965 286456 762261 447568 244822 145562 250236 242320 063586 149944 824070 329700 660425 639346 935957 772023 093242 836858 950068 224883 817716 337189 563143 572191 438094 491083 555456 916369 792833 426614 890094 815772 330900 472922 230442 120972 961278 668931 029620 032755 007511 826275 067641 995443 658291 689366 905791 044095 956506 397881 984724 290730 059674 549998 007844 196960 907791 812308 151404 735080 769016 945886 070263 365951 777102 343886 215992 234789 842505 766364 105328 194053 761841 975720 504800 708988 757431 530082 451282 374765 158081 686135 802773 444359 411028 101007 522013 384748 715809 560187 994668 764704 222972 349477 759132 244831 804427 131329 941903 116539 648926 351465 809537 608908 230251 429031 784443 663813 953006 942723 792668 853530 633758 200572 297712 366463 537275 826498 744248 557063 672431 456478 284687 733482 224768 545196 271445 987069 363960 494689 850706 774974 010358 131218 076840 371946 816684 097602 715114 650823 730313 769040 200180 603267 502342 666391 867546 710823 499218 970089 757329 283640 462860 589069 058383 803525 083407 379017 264164 989615 268028 943671 305051 822819 082387 872804 232558 554446 211357 641572 741057 682042 497133 316685 452818 535026 098939 179299 816516 843931 472964 300895 300535 511746 977172 567578 722020 882689 314429 787860 756184 513641 770726 168207 137621 < 321017 [i]
- extracting embedded orthogonal array [i] would yield linear OA(3283, 1100, F32, 74) (dual of [1100, 1017, 75]-code), but
(9, 9+76, 1101)-Net in Base 32 — Upper bound on s
There is no (9, 85, 1102)-net in base 32, because
- 6 times m-reduction [i] would yield (9, 79, 1102)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 80714 773630 284453 729957 110611 230211 848287 485471 881277 628302 334531 254108 666134 586167 277475 348234 216991 667117 108461 316764 > 3279 [i]