Best Known (230, ∞, s)-Nets in Base 4
(230, ∞, 258)-Net over F4 — Constructive and digital
Digital (230, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (230, 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
(230, ∞, 708)-Net in Base 4 — Upper bound on s
There is no (230, m, 709)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (230, 3539, 709)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43539, 709, S4, 5, 3309), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 11067 085043 807489 687661 255506 708873 310379 588727 293971 171917 811138 408574 582402 201258 789766 795181 961994 791586 199195 252651 658420 278595 014943 951120 311073 798827 236640 203044 631967 935061 046498 193200 177911 765457 818782 718643 259782 727444 151929 094889 119869 533285 878902 937041 794109 266216 952566 121046 557893 104364 351789 995655 532665 319778 331412 023779 265602 544644 352563 227818 431321 137741 250902 503315 243292 838969 493644 861630 499773 407106 996731 948834 745790 319018 787744 976232 353021 874828 172358 209221 430999 649526 925086 714247 057056 226541 447360 807120 479393 689551 563544 263201 422864 342578 325120 825672 501853 935966 381231 874201 998718 371278 052802 394317 906473 379507 408450 004841 104060 392103 436794 521718 575773 446520 069270 659135 901563 454345 553231 959203 898981 061520 973621 081290 837183 104179 701548 072170 347670 237657 709517 158199 921124 530438 741534 095427 793057 196307 879639 956364 484018 846276 737509 730712 489567 708266 137919 492023 556962 342536 670891 061201 261024 598654 980467 477035 861178 574001 648721 027201 674955 761824 101677 509463 969277 464833 817960 643015 711652 839276 178557 748125 837917 975455 052296 098743 763151 551840 439709 888531 939029 983415 654762 072111 221527 790370 668357 351326 473767 071978 685333 643703 298435 139294 826298 627560 994313 765330 512164 332183 812884 420935 252306 185240 037346 139486 033666 806204 158535 995114 848764 366870 739005 017410 291641 115393 873396 022056 100537 372721 231386 144599 070971 734164 130065 901671 926392 679139 670889 471077 975538 228821 679805 375278 308479 098986 408532 918955 055606 024298 988227 964130 792127 680479 707655 489536 026259 427128 296169 420381 841824 627745 379477 822399 919736 934899 791894 361770 944384 316396 092440 614177 036163 226442 608167 623593 647320 339663 426187 820039 897624 938172 880888 185766 420611 555050 850727 168184 863100 516595 134487 937114 461311 956025 108523 658048 115470 286504 739642 857609 847756 800494 803004 981347 212033 260486 792971 809331 944667 809602 124647 296500 629100 744603 922927 362291 012426 673507 242128 510437 530332 346308 296487 914721 766493 896209 793247 691703 039641 033018 560428 904603 887721 731683 953254 209734 224676 755065 779562 359839 717119 188040 559054 285123 490466 715592 149848 583405 079929 579435 492977 047716 530345 875079 340215 850292 258991 056330 231998 130855 990111 674325 554269 757607 832927 076352 / 1655 > 43539 [i]
- extracting embedded OOA [i] would yield OOA(43539, 709, S4, 5, 3309), but