Best Known (43, 43+∞, s)-Nets in Base 8
(43, 43+∞, 98)-Net over F8 — Constructive and digital
Digital (43, m, 98)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (43, 97)-sequence over F8, using
- t-expansion [i] based on digital (37, 97)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 37 and N(F) ≥ 98, using
- t-expansion [i] based on digital (37, 97)-sequence over F8, using
(43, 43+∞, 129)-Net over F8 — Digital
Digital (43, m, 129)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (43, 128)-sequence over F8, using
- t-expansion [i] based on digital (38, 128)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 38 and N(F) ≥ 129, using
- t-expansion [i] based on digital (38, 128)-sequence over F8, using
(43, 43+∞, 324)-Net in Base 8 — Upper bound on s
There is no (43, m, 325)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (43, 971, 325)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8971, 325, S8, 3, 928), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 11003 059445 456576 959225 741552 537553 723816 107431 319602 559372 882959 163554 032333 124747 554110 302891 772174 347936 101436 575471 923331 335635 069048 884614 830213 155224 013190 172726 475146 785039 408471 261417 214292 188888 225804 081168 765846 800154 188154 455605 554702 482090 971108 651513 834280 231813 303311 619869 360059 161844 788234 819716 541689 599605 672396 077047 000351 581448 766729 759789 893530 987898 775865 381872 304335 670633 873481 681098 959687 375281 319545 051133 190033 510435 457286 650344 510869 558775 993049 508559 622735 977425 476847 914051 708707 503574 724043 663652 556967 975413 505657 112718 942907 672035 697396 530810 840368 241828 241046 638044 106991 582208 183064 909971 875726 003519 089419 340651 931302 090634 710513 348892 573497 091187 341748 703713 225073 707465 580717 233492 166130 175731 615668 553220 700896 709703 727691 934991 586836 893625 413929 064009 940931 240222 491100 060963 207957 806854 874559 728277 501964 570244 669911 191407 699206 573526 089728 / 929 > 8971 [i]
- extracting embedded OOA [i] would yield OOA(8971, 325, S8, 3, 928), but