Best Known (4, ∞, s)-Nets in Base 49
(4, ∞, 54)-Net over F49 — Constructive and digital
Digital (4, m, 54)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (4, 53)-sequence over F49, using
(4, ∞, 92)-Net over F49 — Digital
Digital (4, m, 92)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (4, 91)-sequence over F49, using
- t-expansion [i] based on digital (3, 91)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- t-expansion [i] based on digital (3, 91)-sequence over F49, using
(4, ∞, 250)-Net in Base 49 — Upper bound on s
There is no (4, m, 251)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (4, 249, 251)-net in base 49, but
- extracting embedded OOA [i] would yield OA(49249, 251, S49, 245), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 354 013649 449525 931426 279442 990642 053580 432370 765307 807128 294998 551122 640747 634597 271084 333393 795330 500587 164243 140988 540373 888581 863590 044622 404991 728906 599366 400005 917176 740377 601943 975293 629949 119408 598903 469298 568197 261263 089787 497027 712508 751288 114794 103433 426230 872340 717070 631044 534195 535930 764662 142517 697871 788941 015702 182840 766509 295270 854651 459881 610586 893475 184126 853183 587780 497947 092464 128387 019611 820640 300001 / 41 > 49249 [i]
- extracting embedded OOA [i] would yield OA(49249, 251, S49, 245), but