Best Known (248, ∞, s)-Nets in Base 4
(248, ∞, 258)-Net over F4 — Constructive and digital
Digital (248, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (248, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
(248, ∞, 301)-Net over F4 — Digital
Digital (248, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (248, 300)-sequence over F4, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 234 and N(F) ≥ 301, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
(248, ∞, 762)-Net in Base 4 — Upper bound on s
There is no (248, m, 763)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (248, 3809, 763)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43809, 763, S4, 5, 3561), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 39196 836990 698800 023119 593753 309924 865666 836820 821407 429587 269285 049295 252967 712165 840467 237381 747223 534372 885791 897843 594024 292249 282164 972309 913864 559891 719188 573773 173478 813394 627663 271422 764100 842534 583456 786135 594410 392016 501939 748254 795552 852254 771633 890198 282762 226003 909846 541985 520673 440279 505670 950554 973694 340175 891253 420512 407738 556005 411861 893949 942393 638352 126659 582358 419911 461380 513544 643614 830268 276563 260547 909457 319964 973857 164864 430396 960461 859204 607297 635172 558026 654822 645719 232098 177387 478430 257757 685550 060757 954258 509818 650624 307461 030244 863605 123482 162573 553735 840558 816199 882755 606327 825584 895096 651810 729098 548302 842552 600906 972297 811920 741059 615710 903220 647575 063090 041682 375400 840635 893786 957969 042553 956835 070740 343298 514819 608301 160250 126200 149166 549384 898336 835235 411665 401953 437792 406900 917568 336533 873831 997164 009236 106390 654099 732284 391722 147507 743358 733885 844375 976253 863021 704145 223021 702553 485657 254027 310013 005937 338589 260799 217538 137315 138247 451207 097149 327765 071215 911301 207438 581449 564794 511498 175436 467322 503736 307084 938943 817788 472580 236411 193120 288378 465889 103600 501579 042309 926160 496115 102548 114402 576734 466074 900670 470807 820138 154613 093486 934908 915577 762116 278534 863022 971472 197124 561222 460456 057991 893668 004741 243802 127872 251554 516804 416149 965178 010564 156724 085650 616492 618575 433880 680652 310212 557783 868365 675182 527843 207160 228680 103220 425094 134986 215298 442354 224357 372083 766997 450396 271701 485373 800543 968211 357792 495269 943954 167476 774214 249007 639742 258053 825659 934568 319704 749569 043334 668786 820143 232916 347409 953607 629668 094848 818967 890522 379901 382596 153845 143333 218381 860236 358268 494809 003121 154757 413484 267667 590361 957510 098807 427187 415162 979474 886268 617041 232612 638814 733761 159484 000914 392613 457439 690614 414964 968901 682724 934269 490796 999736 203301 817832 525140 876466 873112 274877 965453 899970 588756 732256 583898 421628 421308 776745 974209 308400 348322 863015 455985 852429 730962 200691 831749 960508 479944 701707 836653 096868 003552 559069 539087 624744 430289 064322 559856 371599 171480 873631 456935 976618 090340 600057 687105 098881 791130 197160 782174 226274 848268 769723 723421 678160 560997 130692 192305 117816 371583 246168 515432 065014 679430 299450 822074 650644 400923 448762 761622 860405 710084 525978 858039 500773 365318 573480 537975 608799 324711 507611 148568 089827 093552 982948 772701 011968 / 1781 > 43809 [i]
- extracting embedded OOA [i] would yield OOA(43809, 763, S4, 5, 3561), but