Best Known (155, 155+∞, s)-Nets in Base 4
(155, 155+∞, 130)-Net over F4 — Constructive and digital
Digital (155, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (155, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
(155, 155+∞, 215)-Net over F4 — Digital
Digital (155, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (155, 214)-sequence over F4, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 148 and N(F) ≥ 215, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
(155, 155+∞, 482)-Net in Base 4 — Upper bound on s
There is no (155, m, 483)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (155, 2409, 483)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42409, 483, S4, 5, 2254), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 79 540789 270263 705801 537337 796078 783529 400539 852108 937134 881922 802115 957937 271766 020348 606253 421057 007999 152077 953330 075007 103802 025350 709448 523595 078376 617068 289612 204714 403906 761684 056464 072971 606555 981794 909297 511919 987622 557795 374245 397366 390192 599392 244906 703322 539076 645181 788527 159201 489075 887095 613001 430695 978269 285890 769828 468534 299723 049114 589497 282935 236179 897310 034119 323411 375518 545479 458220 704758 013714 226510 862159 672724 106765 235149 126010 610470 308559 410406 559432 755370 862379 762794 137978 401302 506389 248265 971288 698872 089772 026521 290246 087013 768093 658492 502494 140231 658323 130205 062884 826374 441860 427508 780012 934743 672766 456577 212648 043807 648045 534744 413530 717528 891092 065397 166539 330251 592341 240488 097895 248302 746910 487672 981659 886222 083471 237073 771421 967064 721629 317178 023228 705095 627496 875829 386066 389221 656047 894099 310856 986247 766002 674031 104752 656314 787409 648556 370732 800194 093209 351682 372415 581315 891770 815699 119511 376423 773242 568065 793954 919120 023632 437360 013304 075390 993248 494255 662579 646184 999389 036792 351374 872240 907389 974880 946137 098515 656561 140978 068918 298472 630068 000893 827799 545461 690209 929351 450588 803006 445234 173719 845252 259176 788190 004153 867419 133066 888264 346030 338563 441607 952890 579094 013286 743181 646487 273669 301993 414083 923881 571636 953164 515958 201698 146166 370340 399140 049616 502766 236052 084211 493722 942723 559441 609896 550273 988813 729318 875891 878179 892295 032000 037021 079718 739271 947102 056708 346092 473426 015097 294013 171486 425088 / 2255 > 42409 [i]
- extracting embedded OOA [i] would yield OOA(42409, 483, S4, 5, 2254), but