Best Known (5, 5+∞, s)-Nets in Base 64
(5, 5+∞, 128)-Net over F64 — Constructive and digital
Digital (5, m, 128)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
(5, 5+∞, 133)-Net over F64 — Digital
Digital (5, m, 133)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (5, 132)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 133, using
(5, 5+∞, 390)-Net in Base 64 — Upper bound on s
There is no (5, m, 391)-net in base 64 for arbitrarily large m, because
- m-reduction [i] would yield (5, 389, 391)-net in base 64, but
- extracting embedded OOA [i] would yield OA(64389, 391, S64, 384), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 257 151968 807345 829051 020589 828520 018641 242524 356395 099408 083902 128237 132239 124488 398156 224805 871321 755095 136452 926004 914692 767200 552304 151162 188205 324363 261239 934262 155567 876640 496645 522564 639118 787979 671023 910594 197462 889745 719058 678165 004956 033763 475669 544779 510277 929294 095121 196024 702209 621724 728272 338892 034505 371239 717511 341206 102459 360476 396042 721571 426601 851041 581693 063222 446584 978542 660456 575345 220233 489667 525374 356413 497682 380055 123271 241797 666217 979221 296206 761170 095646 525614 298883 118782 244743 739569 581556 052203 726815 363266 894471 037587 801628 105188 400993 255699 075764 529893 364309 124115 898585 647734 244652 511137 625826 146012 375288 260597 317727 793577 754922 692085 244125 741894 913750 982116 357257 035776 / 55 > 64389 [i]
- extracting embedded OOA [i] would yield OA(64389, 391, S64, 384), but