Best Known (16, 16+∞, s)-Nets in Base 25
(16, 16+∞, 126)-Net over F25 — Constructive and digital
Digital (16, m, 126)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (16, 125)-sequence over F25, using
- t-expansion [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- t-expansion [i] based on digital (10, 125)-sequence over F25, using
(16, 16+∞, 150)-Net over F25 — Digital
Digital (16, m, 150)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (16, 149)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 16 and N(F) ≥ 150, using
(16, 16+∞, 434)-Net in Base 25 — Upper bound on s
There is no (16, m, 435)-net in base 25 for arbitrarily large m, because
- m-reduction [i] would yield (16, 867, 435)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(25867, 435, S25, 2, 851), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 129 091465 661372 995210 002538 629707 754231 533073 735217 510561 593335 162014 804167 147660 332691 208465 565923 867252 549831 065451 612551 330780 552164 583803 538660 468113 762474 898485 552310 190060 355472 719280 343737 640452 353399 944771 100084 835989 268780 696571 767954 224866 360205 729543 017383 780070 420751 994772 325239 477424 266883 951720 554287 379485 775512 370730 715788 145998 152982 342146 829059 358934 751271 859073 588814 052860 880750 443138 689287 013331 297899 161469 505688 118279 682155 499319 898740 811734 262548 432803 174888 852928 829675 640002 101495 291527 752259 744884 281382 615698 988951 278122 952866 323162 086684 802102 965209 135511 694277 832745 806190 216785 523892 969112 157523 192397 536913 494791 475393 915386 250208 385380 129451 781161 179475 431640 013331 415008 436284 529274 303280 559592 095320 936649 822756 965245 762541 166300 153653 842653 440426 293746 116691 997622 685111 367635 863287 472254 926277 254496 037220 260725 818178 698694 642112 392507 303947 949284 009643 400613 309628 617559 883946 635932 217301 203664 158738 916896 505877 869127 596586 144091 272079 246348 760423 727297 968419 147710 152588 843727 994053 093232 738079 336677 405603 333866 463830 655797 103091 092138 187677 127359 847301 950505 727184 860350 791555 473453 223695 522147 273062 538258 151691 522312 185852 943496 218447 894108 294349 280185 997486 114501 953125 / 71 > 25867 [i]
- extracting embedded OOA [i] would yield OOA(25867, 435, S25, 2, 851), but