Best Known (38, 38+∞, s)-Nets in Base 8
(38, 38+∞, 98)-Net over F8 — Constructive and digital
Digital (38, m, 98)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (38, 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
(38, 38+∞, 129)-Net over F8 — Digital
Digital (38, m, 129)-net over F8 for arbitrarily large m, using
- net from sequence [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
(38, 38+∞, 288)-Net in Base 8 — Upper bound on s
There is no (38, m, 289)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (38, 863, 289)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8863, 289, S8, 3, 825), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 13 957576 743605 502644 200628 719882 505923 882533 377668 472694 137694 013700 796570 281602 215572 140165 010711 629540 441502 972510 830518 709419 977759 588742 113832 993622 969962 743738 715863 399244 682558 251184 295283 709411 197948 685886 191014 789209 677522 470443 117803 271221 853431 573044 896047 995643 021592 684302 383262 816607 258809 237038 535505 953750 608709 145339 144727 444460 476570 752450 204417 233500 156719 963031 355043 429629 938943 335699 959591 078731 395720 073542 013333 120962 523728 899923 813139 105282 748797 209211 071120 797510 875465 982526 784753 019135 514301 385811 639017 261493 803013 689238 336256 638837 706720 271314 037604 311382 318475 261234 865882 715320 625961 415386 344510 501171 181374 123395 210510 436962 656439 283977 114959 458557 042541 913653 072071 641540 966376 760313 734635 918059 232156 987207 509014 836229 556274 515157 097242 535101 726720 / 59 > 8863 [i]
- extracting embedded OOA [i] would yield OOA(8863, 289, S8, 3, 825), but