MinT - Best Known (105−92, 105, s)-Nets in Base 32

Best Known (105−92, 105, s)-Nets in Base 32

(105−92, 105, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 105, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 105, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(105−92, 105, 129)-Net over F₃₂ — Digital

Digital (13, 105, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 105, 129)-net over F₃₂, using
- net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(105−92, 105, 1550)-Net over F₃₂ — Upper bound on s (digital)

There is no digital (13, 105, 1551)-net over F₃₂, because

extracting embedded orthogonal array [i] would yield linear OA(32¹⁰⁵, 1551, F₃₂, 92) (dual of [1551, 1446, 93]-code), but
- the Johnson bound shows that NÂ â‰¤ 27561 245513 393854 586113 861788 744725 215438 702371 235548 301449 384948 646237 636392 938883 318391 492185 548187 590152 102823 216009 281302 937575 018655 529133 152516 747322 572724 886389 415287 974560 086009 775908 003906 400764 972109 317217 956327 485699 106967 148933 653037 092239 592903 150452 042970 141245 446291 805983 033312 989778 590536 302018 286653 130858 945269 895623 151893 915168 387036 508255 979548 272432 156796 327920 588834 509346 718569 209543 039931 404396 686378 710236 007403 754971 018969 804606 719094 419892 225644 938153 933791 222032 779930 079452 842404 241629 623440 183708 159181 964606 300117 918542 577460 639217 591276 817996 606277 031423 115124 432440 278610 735596 440764 080536 899957 250003 276187 429763 714858 694030 149105 458423 773276 483131 754817 263943 303367 272597 361855 350588 428153 896083 674726 366082 432894 132522 118602 687348 198354 746365 544351 248311 432143 188708 755652 136203 699743 924208 270338 631607 708930 482256 724675 035834 774334 784714 126112 351033 287543 344955 039206 769022 857012 871487 032556 025518 333227 708627 804986 388866 224039 044438 191482 171135 894548 834697 611431 153279 812489 402081 151458 272626 080417 372600 058427 499918 389780 301538 520837 201496 969023 120492 231699 338630 272490 503224 014460 088913 879499 993979 210218 583923 987736 822224 783887 358328 957769 690246 172654 337397 256538 871542 631150 800044 428287 334050 625810 699208 022181 926625 166202 155801 283598 762972 335290 683128 778657 783562 507869 469649 191172 253179 445573 662119 970232 304314 937342 593201 111229 159387 127971 258584 485259 546205 585403 709450 561168 864353 601529 552450 942624 178601 279246 815446 211832 734357 290547 429335 806163 054159 605908 475912 659954 899158 513685 475592 940115 366514 917101 568139 159267 069713 833784 810320 473297 643577 387228 720783 634428 301331 291315 625449 376363 219122 770178 946120 073416 642975 758425 699697 928707 117694 305492 739015 792131 950739 592969 075093 494820 885667 488776 322832 716181 847628 831647 734781 345725 332443 123491 964079 439017 437460 384253 879715 286924 543840 056402 683986 015637 134394 615562 276690 834218 763813 768293 332991 689503 130735 957029 121537 677180 850329 521092 784476 629323 305585 160138 884724 246323 066866 099349 883207 224794 380682 667197 934058 852460 168760 666173 065321 381505 840984 122627 976721 537696 547855 817486 055529 883719 292058 653169 948686 499061 041778 869525 252681 948052 804550 339079 238269 202355 303738 102479 < 32¹⁴⁴⁶ [i]

(105−92, 105, 1559)-Net in Base 32 — Upper bound on s

There is no (13, 105, 1560)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 112 106154 277465 332695 337701 928278 576899 003729 009240 961894 968744 074808 999177 219627 620792 338003 084019 091032 882592 561190 817160 747721 304079 074514 567258 515819 856352 > 32¹⁰⁵ [i]

Best Known (105−92, 105, s)-Nets in Base 32

(105−92, 105, 120)-Net over F32 — Constructive and digital

(105−92, 105, 129)-Net over F32 — Digital

(105−92, 105, 1550)-Net over F32 — Upper bound on s (digital)

(105−92, 105, 1559)-Net in Base 32 — Upper bound on s

(105−92, 105, 120)-Net over F₃₂ — Constructive and digital

(105−92, 105, 129)-Net over F₃₂ — Digital

(105−92, 105, 1550)-Net over F₃₂ — Upper bound on s (digital)