MinT - Best Known (103−90, 103, s)-Nets in Base 32

Best Known (103−90, 103, s)-Nets in Base 32

(103−90, 103, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 103, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 103, 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]

(103−90, 103, 129)-Net over F₃₂ — Digital

Digital (13, 103, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 103, 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]

(103−90, 103, 1553)-Net over F₃₂ — Upper bound on s (digital)

There is no digital (13, 103, 1554)-net over F₃₂, because

extracting embedded orthogonal array [i] would yield linear OA(32¹⁰³, 1554, F₃₂, 90) (dual of [1554, 1451, 91]-code), but
- the Johnson bound shows that NÂ â‰¤ 928212 485551 059910 571755 851738 572407 207009 781306 916491 954687 462235 308811 682108 034761 677534 309575 700938 848913 961740 017042 624132 443352 844676 333168 956742 751574 622414 829894 119378 932551 420348 164956 182623 248796 987227 971414 744031 260767 740908 186590 174513 642632 255414 681839 839220 475612 269672 360617 734691 350424 850890 159055 927356 198745 857556 182361 873976 000725 992675 322960 830868 028103 584664 820184 618152 037577 938601 975785 939757 161844 304669 412291 242845 235987 956450 514314 956798 961143 205781 517386 317631 140186 531139 277111 673779 981680 784719 432986 039224 017812 980787 063574 248172 368721 779602 909403 877259 607158 403016 898062 710006 166224 486934 553549 004326 132882 938933 045971 299886 182090 641110 169645 936794 187577 496831 090513 744246 916292 478208 769228 998875 678774 475076 106235 198040 789646 744395 255216 234671 923293 231738 168549 679083 815646 425501 024380 177936 610032 041112 333329 738855 159274 649434 371241 605298 594550 941815 360652 201785 277773 666991 901740 354358 935164 322394 103050 654788 713166 180929 354007 419556 570120 776988 097531 785687 158345 872741 109264 228425 431149 438502 905250 679176 097718 913151 038179 889133 664358 657375 637687 818231 888704 144471 820978 914050 513310 001831 127954 206700 911292 967486 763022 961312 181111 969652 220365 727254 317404 888682 967510 169692 707883 362838 216977 192115 568341 932065 783581 502552 302609 231168 126025 984540 298502 785109 542418 388462 925311 359409 706011 203852 588523 377135 013761 580873 819921 031892 722397 412481 225067 398376 092217 909784 645662 520646 597492 611440 361388 707626 831816 723098 972297 846430 481701 308472 883918 151402 878440 516743 627556 691717 978730 891931 642987 458031 814601 468022 862964 406258 802486 229000 102993 347868 528357 939286 738179 161392 659971 946160 786383 491325 413385 530750 669142 442332 000043 537379 883039 207206 605737 158206 288381 882307 640749 549060 919389 161512 595462 647251 969246 182318 253788 245850 332594 373687 166380 101327 563673 279299 883155 331821 653825 504816 454618 285557 037023 021373 698397 920359 863198 290927 677573 305248 234918 835821 648700 312884 383285 651074 999755 493496 184087 972655 239714 176563 862522 362428 965082 672643 832962 948027 667609 760151 595290 134434 266072 426440 364335 544470 029767 370849 727473 557312 621511 592183 921762 144085 089997 404061 971434 553168 937702 418096 715268 401840 623708 234403 006608 391749 285668 254874 470992 154383 031262 < 32¹⁴⁵¹ [i]

(103−90, 103, 1561)-Net in Base 32 — Upper bound on s

There is no (13, 103, 1562)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 109506 373532 121206 940681 810331 225826 863130 691189 393134 683502 080133 488689 418268 338884 264570 968431 232313 255912 537917 591252 572062 581406 143254 888833 332842 703936 > 32¹⁰³ [i]

Best Known (103−90, 103, s)-Nets in Base 32

(103−90, 103, 120)-Net over F32 — Constructive and digital

(103−90, 103, 129)-Net over F32 — Digital

(103−90, 103, 1553)-Net over F32 — Upper bound on s (digital)

(103−90, 103, 1561)-Net in Base 32 — Upper bound on s

(103−90, 103, 120)-Net over F₃₂ — Constructive and digital

(103−90, 103, 129)-Net over F₃₂ — Digital

(103−90, 103, 1553)-Net over F₃₂ — Upper bound on s (digital)