Best Known (41, 41+∞, s)-Nets in Base 8
(41, 41+∞, 98)-Net over F8 — Constructive and digital
Digital (41, m, 98)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (41, 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
(41, 41+∞, 129)-Net over F8 — Digital
Digital (41, m, 129)-net over F8 for arbitrarily large m, using
- net from sequence [i] based on digital (41, 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
(41, 41+∞, 310)-Net in Base 8 — Upper bound on s
There is no (41, m, 311)-net in base 8 for arbitrarily large m, because
- m-reduction [i] would yield (41, 929, 311)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(8929, 311, S8, 3, 888), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 18 690800 895803 493811 194214 480008 129174 159843 468675 670793 932807 407469 876422 259133 797281 220723 182288 999678 987162 837029 277238 625788 799608 436713 662373 676569 127377 218456 299020 729201 778400 862300 173719 102900 062177 396159 312911 085946 065854 448711 924896 720017 634245 229136 750394 296526 383199 242729 062274 103004 074630 541033 679602 494600 622431 677461 508046 139895 280945 979574 040059 311513 519976 029430 717617 857139 377524 866874 274574 317627 576621 232310 654249 591053 662497 652372 242120 764326 473836 932127 825670 243049 379140 846751 517276 974286 344604 194468 172410 741679 341445 655792 214028 831493 513561 041195 238922 838212 849945 889611 280396 456510 051860 754887 264123 020792 705533 089886 527043 035908 960277 415382 416234 906758 332678 507824 225559 539737 914584 172002 609808 225454 516517 387367 972601 591596 637590 684726 979953 961165 251845 252845 002947 058710 721773 485992 969856 143565 999002 390993 305600 / 127 > 8929 [i]
- extracting embedded OOA [i] would yield OOA(8929, 311, S8, 3, 888), but