Best Known (183, 183+∞, s)-Nets in Base 4
(183, 183+∞, 200)-Net over F4 — Constructive and digital
Digital (183, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (183, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the 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) = 161 and N(F) ≥ 200, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
(183, 183+∞, 220)-Net over F4 — Digital
Digital (183, m, 220)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (183, 219)-sequence over F4, using
- t-expansion [i] based on digital (181, 219)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 181 and N(F) ≥ 220, using
- t-expansion [i] based on digital (181, 219)-sequence over F4, using
(183, 183+∞, 566)-Net in Base 4 — Upper bound on s
There is no (183, m, 567)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (183, 2829, 567)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42829, 567, S4, 5, 2646), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 564 237483 149637 484578 301991 209263 008380 467723 095954 877521 070213 373013 544363 489703 912095 183319 946874 917608 104077 014131 811723 406145 835265 469590 376276 560590 760742 310539 119177 927391 649962 397502 330215 262699 716183 171883 729416 372494 009528 871198 558106 919778 737321 945374 771981 312261 476370 413472 328713 080630 319838 763010 431047 641516 130150 773013 946241 125142 718422 795664 276447 930456 287799 631594 132461 503400 480926 155415 744290 629640 933080 621140 599570 078176 894653 276738 320362 292328 361537 489719 272257 465896 263796 208078 333232 635534 894133 750978 124128 006489 867864 254189 163734 005653 047070 281753 669771 788962 678613 230330 010869 493337 809205 271265 354763 161264 567131 211866 650978 716662 281345 612966 244604 243731 340567 475095 800884 515125 846288 724376 987161 399034 511527 049354 536309 757764 350310 912942 990486 910115 899030 598603 948377 580290 317002 243500 524723 457243 393921 919790 551913 251310 266518 537198 147236 119820 549449 298717 001957 709406 197023 831691 100710 251098 447521 995554 878547 321598 162947 888953 029853 126458 106106 612685 172932 624733 071488 439154 468126 592964 137982 989298 732977 293796 217767 284546 184199 710573 136686 952441 624498 989573 054472 918037 703768 756653 837338 286857 439934 283802 105806 342575 429844 335334 526816 096137 028306 817992 139141 508865 622264 279643 366641 808317 027246 337773 812606 065708 280135 041621 333712 951845 630702 386704 671638 609278 188384 898538 274294 608262 555060 545927 834812 304607 255673 096637 711729 306264 848634 512531 653728 359408 097866 422557 973076 075115 252874 789060 981832 736349 571201 678626 611865 042106 377500 389853 971866 094530 707980 999585 455633 806020 514904 838627 946945 744465 748556 901614 310222 091035 640362 076044 436248 592498 247372 881612 202577 739706 283514 066169 978277 405282 002667 590727 759901 388267 297157 049208 665458 692131 084463 708539 447276 630662 184960 / 2647 > 42829 [i]
- extracting embedded OOA [i] would yield OOA(42829, 567, S4, 5, 2646), but