MinT - Best Known (154−90, 154, s)-Nets in Base 3

Best Known (154−90, 154, s)-Nets in Base 3

(154−90, 154, 48)-Net over F₃ — Constructive and digital

Digital (64, 154, 48)-net over F₃, using

t-expansion [i] based on digital (45, 154, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(154−90, 154, 64)-Net over F₃ — Digital

Digital (64, 154, 64)-net over F₃, using

t-expansion [i] based on digital (49, 154, 64)-net over F₃, using
- net from sequence [i] based on digital (49, 63)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
    - a curve from the manYPoints database [i]

(154−90, 154, 297)-Net in Base 3 — Upper bound on s

There is no (64, 154, 298)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁵⁴, 298, S₃, 90), but
- 2 times code embedding in larger space [i] would yield OA(3¹⁵⁶, 300, S₃, 90), but
  - the linear programming bound shows that MÂ â‰¥ 75144 567345 687525 639879 678310 953136 444220 630389 117224 769406 822044 912599 522554 587335 516843 374410 421022 727858 531491 595134 595654 546025 118753 082871 565895 460474 775853 613744 419010 460478 303465 634150 186065 224183 205141 648966 235856 633157 183951 570400 364758 812952 499427 996861 204369 897006 933987 249656 888197 060834 862350 085670 736242 313761 769086 663122 441227 057439 778964 799674 357003 956829 397930 599512 227545 945025 808950 467939 469509 190009 849770 308476 047950 024745 505774 159014 864804 004582 556654 827211 946269 289664 678362 713110 209194 597812 819709 373520 006602 562078 650512 544265 060489 914967 873146 961862 772449 134763 041860 686184 160913 342509 375501 543266 657443 635792 189511 768705 969837 906925 939397 537768 877718 859685 045531 014912 399461 196130 873804 455934 732692 759188 630517 910290 896789 684917 950007 151289 070798 923122 673283 232352 667373 690303 786113 637738 906198 029702 752533 850957 098653 462171 077029 284300 909620 442056 205666 668841 981013 492220 150763 446606 958196 917404 527648 834774 681147 589314 575458 157137 977023 389413 516052 002535 798234 343421 384049 726956 752192 223020 624016 266624 918268 197862 693604 296927 819357 703725 533401 781441 956104 640765 904393 257781 085781 618927 376142 079684 861505 360405 258496 125515 158763 301887 988137 675262 783304 024390 685196 825463 415315 054789 409824 729340 604502 919943 227898 219153 161302 347045 768210 263545 147700 930456 518090 518154 590020 231488 850801 790362 854510 454421 518301 123950 580731 040495 676526 800568 934623 651811 428981 836928 326126 597476 747931 / 150 070396 612338 202568 627606 819005 341324 999018 375143 031907 825898 830879 295487 237815 081284 498815 750070 423717 823220 192071 848537 320915 671243 448746 319396 996247 726875 708247 327842 030082 406650 254725 380460 855168 334587 179353 553741 218133 187177 137860 274023 471961 692581 438533 288429 677810 613203 046224 124321 169262 921649 492967 859372 598042 646150 998120 638692 925743 001505 912812 655826 953359 253256 364201 208422 876731 492746 336795 529610 337185 955236 900151 922757 729225 965974 606171 871075 452800 076970 279261 609541 368373 233148 798740 535798 779702 283400 392309 781347 656822 874902 073858 050422 846139 961312 714150 815812 132409 276445 098300 767695 554591 721182 189072 474939 543744 989543 998765 016027 980969 215222 851882 762577 105621 980164 544457 555999 069211 672995 660207 254046 391373 840419 972163 330415 899914 190876 481605 250397 123538 456501 031291 283912 674534 140648 446406 404617 310312 026843 083321 141741 776081 402983 808524 850527 876057 397750 302115 136842 032174 836791 432910 660318 904394 291199 634095 592283 048166 785869 516516 163152 295717 662583 082776 625577 016647 965606 335036 882257 916816 123558 394968 400299 271473 837136 011817 437124 289871 446854 764282 760719 867822 674794 705918 644729 565256 298505 912617 909021 601232 829437 136320 156350 988939 000365 613427 272132 376935 415705 137294 788738 861566 504123 291199 943181 484951 132077 571014 324310 324087 134770 564243 229008 755924 360161 854849 310397 097049 543274 289510 659471 438909 858187 > 3¹⁵⁶ [i]

Best Known (154−90, 154, s)-Nets in Base 3

(154−90, 154, 48)-Net over F3 — Constructive and digital

(154−90, 154, 64)-Net over F3 — Digital

(154−90, 154, 297)-Net in Base 3 — Upper bound on s

(154−90, 154, 48)-Net over F₃ — Constructive and digital

(154−90, 154, 64)-Net over F₃ — Digital