Best Known (42, ∞, s)-Nets in Base 8
(42, ∞, 98)-Net over F8 — Constructive and digital
Digital (42, m, 98)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (42, 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
(42, ∞, 129)-Net over F8 — Digital
Digital (42, m, 129)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (42, 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
(42, ∞, 317)-Net in Base 8 — Upper bound on s
There is no (42, m, 318)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (42, 950, 318)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8950, 318, S8, 3, 908), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 399 949927 962756 002496 577181 449265 121626 894540 210512 562353 230700 915028 779759 296245 800940 906029 578973 053826 239118 369633 228657 501479 629402 566447 477273 167379 737691 666812 366607 005256 485558 754861 924802 348297 592720 791987 508138 770654 533954 343491 826769 814731 122132 101461 813152 423193 805595 374279 812068 799614 062650 636604 528575 402339 193715 128733 592996 503780 032897 121207 151486 198244 577172 073591 655600 715765 061903 063305 694310 273380 257332 872074 682353 818282 832809 008457 750004 169975 480047 214270 475483 900205 367319 980796 768188 052529 584671 089791 432955 105499 307765 579543 402650 616485 201218 592783 218900 840140 629154 967718 522798 563291 997532 082653 997412 869643 069320 368265 157948 106900 548647 449052 561738 310615 346994 288790 136941 824303 573316 701266 627039 967370 455292 740156 302760 428853 561135 451502 236001 716315 227067 955939 423843 054650 065067 975497 496295 553254 472087 256311 372814 058052 255047 745536 / 303 > 8950 [i]
- extracting embedded OOA [i] would yield OOA(8950, 318, S8, 3, 908), but