Best Known (238, 238+∞, s)-Nets in Base 4
(238, 238+∞, 258)-Net over F4 — Constructive and digital
Digital (238, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (238, 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
(238, 238+∞, 301)-Net over F4 — Digital
Digital (238, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (238, 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
(238, 238+∞, 732)-Net in Base 4 — Upper bound on s
There is no (238, m, 733)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (238, 3659, 733)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43659, 733, S4, 5, 3421), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 329 072708 397499 009791 213426 737055 961664 789738 241863 748352 873571 857445 232341 302664 219628 041208 590271 673344 530720 562257 567992 775981 775193 906383 176011 598666 049340 604382 314405 261816 815096 318468 682932 606429 564087 201625 441532 336113 849386 706672 712900 571283 622078 503372 095768 907771 564165 184749 530324 261290 423441 275419 104821 302518 083633 669356 521058 185733 303351 305112 441309 305980 383968 608316 500533 558103 906603 650870 210798 167288 274771 816307 686487 921627 258452 281327 438993 349167 236745 719757 982436 824234 870556 655798 950811 354495 043411 400510 177164 071076 632222 792063 361788 407014 197702 882925 821712 026374 039130 344301 953060 177740 192588 504005 648253 301847 864963 161527 694139 764711 217097 407189 526418 655171 394344 564039 961776 664393 061299 474540 291426 547441 517976 639670 251016 559463 966026 177335 024797 505642 888651 684919 490586 988325 291215 271390 068848 049468 537775 820369 520586 206749 552922 059195 803031 610450 493543 287530 223052 050361 014462 089857 221667 171960 808518 161601 969387 279235 302818 638218 111976 981063 157214 918908 758782 420208 209411 040246 822723 176752 065664 762900 318009 375602 672858 395152 895752 559658 828545 255291 784219 023360 618498 127411 759415 514482 650966 496324 935738 266942 552394 533815 529705 192981 257327 118544 869836 230430 257084 390507 176806 649371 146421 717704 716561 198354 778266 278859 624951 473937 080024 864830 529693 129467 472308 598673 989754 794968 288033 023008 232024 075227 154009 590108 765349 561076 414185 532184 484696 172872 561523 706475 841412 535937 835606 940127 650986 987700 757197 516452 781070 452348 235316 132720 041088 260852 475616 575527 447618 546397 323401 989470 098491 771055 607417 594006 189059 904399 062988 304673 790902 494596 608152 185020 437509 303513 875286 641065 204353 416398 582384 181019 680909 044583 971078 398599 935180 001869 088732 520148 092526 203799 464481 845066 089154 963164 126488 283338 703226 906379 328625 812060 537178 270744 345571 904051 217306 505519 214690 639122 057409 143185 214893 083993 842191 533309 813097 226369 360603 167124 095507 997899 548487 275307 744481 771721 226823 678091 167534 811558 701681 814053 899269 653986 380199 147884 098781 151241 993619 411546 502610 038362 745754 120712 874975 161486 573752 106586 553270 123748 954662 662047 945912 154162 070955 398933 362402 745782 061682 422359 271502 117841 885466 063018 686702 598196 803492 959247 984978 089642 028725 905047 554352 258074 681052 906857 289557 737472 / 29 > 43659 [i]
- extracting embedded OOA [i] would yield OOA(43659, 733, S4, 5, 3421), but