Best Known (93, 93+∞, s)-Nets in Base 4
(93, 93+∞, 104)-Net over F4 — Constructive and digital
Digital (93, m, 104)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (93, 103)-sequence over F4, using
- t-expansion [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 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) = 73 and N(F) ≥ 104, using
- t-expansion [i] based on digital (73, 103)-sequence over F4, using
(93, 93+∞, 144)-Net over F4 — Digital
Digital (93, m, 144)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (93, 143)-sequence over F4, using
- t-expansion [i] based on digital (91, 143)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 91 and N(F) ≥ 144, using
- t-expansion [i] based on digital (91, 143)-sequence over F4, using
(93, 93+∞, 295)-Net in Base 4 — Upper bound on s
There is no (93, m, 296)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (93, 1178, 296)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(41178, 296, S4, 4, 1085), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3235 720594 129577 520516 035592 000362 484801 114254 634376 173083 171829 096220 550097 266394 559020 738984 495924 968047 653615 160062 353146 596721 035994 531308 511915 034394 372215 103706 488440 901794 224926 905624 868343 466694 858282 816902 654386 164936 085292 070186 578841 336714 843164 023040 637230 279849 821029 638913 577729 875715 544074 752312 647682 049836 696350 065398 361109 116450 769482 713773 762645 550693 330784 625538 481803 485524 184770 967390 275818 619939 381043 293807 676949 592184 171271 187670 755826 205359 398695 609608 330551 814910 468787 981922 532772 937554 962596 627946 900589 756235 365642 352516 000159 904312 393118 849054 968826 412369 572485 649547 429704 129902 999849 018223 765659 322572 869163 157729 116404 866543 055349 801311 723332 727198 412976 197883 697125 842550 259712 / 181 > 41178 [i]
- extracting embedded OOA [i] would yield OOA(41178, 296, S4, 4, 1085), but