Best Known (226, ∞, s)-Nets in Base 4
(226, ∞, 258)-Net over F4 — Constructive and digital
Digital (226, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (226, 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
(226, ∞, 696)-Net in Base 4 — Upper bound on s
There is no (226, m, 697)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (226, 3479, 697)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43479, 697, S4, 5, 3253), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 8355 447899 545083 127971 936582 284803 302407 137305 645488 183087 617023 118946 768787 926730 212174 832183 392566 217076 587072 264649 342420 556464 392211 392011 293378 762861 156359 367662 872626 982375 547947 840825 373475 088494 191669 556547 187817 131703 320147 709805 229959 918707 469101 261970 441874 256410 912101 755440 549751 778428 112447 599306 675474 190005 673511 765802 920041 672790 094032 948631 359117 439503 499601 545283 244647 425716 388486 785618 316347 972083 845232 761302 125410 765610 777742 272512 358553 986456 811778 891593 864014 859364 617122 279431 244605 040834 724367 771577 821859 244337 571502 008196 513473 670171 395630 238219 480092 142973 456953 964026 199495 864935 083329 137595 132474 823854 326659 326728 506336 050762 904689 301776 205928 226219 812118 765248 969046 246785 108948 484384 155031 243292 457215 433128 044661 417481 364187 560901 220427 437433 781644 561914 286854 603575 135553 167749 704474 834376 726325 225634 804537 331487 862417 535653 807887 554335 382580 864976 498248 403027 989884 603072 796187 913017 368477 023462 012010 138846 907476 291895 024895 383034 855344 331828 365796 449477 311540 064762 707181 331057 853643 998056 612970 163618 879860 493651 607390 278647 056384 564026 825383 367198 840185 070912 148033 932984 700226 784658 327562 544869 388626 610287 885070 806677 704969 699784 181851 274199 774034 361621 226343 499461 577869 379541 381178 811001 477243 229964 054146 419155 163553 963472 052896 436399 744082 103270 829152 166556 418945 094399 110679 409776 751484 422598 435198 092677 956404 674478 719188 718668 865180 616283 343380 248412 612010 841514 430583 406045 327822 170578 356797 256527 844040 378255 016109 610759 751819 213377 063329 308950 719731 804378 363544 445360 438910 584512 448543 621548 695712 347604 219644 771736 889374 984292 365378 636603 621874 503545 437731 463881 794775 168747 206659 914283 343212 190026 963745 914185 101055 449222 829729 140541 890919 828791 946076 914576 524286 894457 720484 039918 694725 842411 237740 576208 607988 581218 567027 260818 828730 885839 612210 634786 397712 074074 773031 875093 344927 717594 733553 381264 364646 106897 175527 396579 924860 894177 912433 790861 593325 200891 746813 281325 775137 538817 356310 382778 312773 712396 268893 398450 978979 835417 592240 488113 257454 745028 915396 989027 786124 800596 392836 635956 850967 733903 804356 193926 486136 543275 679590 907904 / 1627 > 43479 [i]
- extracting embedded OOA [i] would yield OOA(43479, 697, S4, 5, 3253), but