Best Known (108, 108+∞, s)-Nets in Base 5
(108, 108+∞, 91)-Net over F5 — Constructive and digital
Digital (108, m, 91)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (108, 90)-sequence over F5, using
- base reduction for sequences [i] based on digital (9, 90)-sequence over F25, using
- s-reduction based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- s-reduction based on digital (9, 103)-sequence over F25, using
- base reduction for sequences [i] based on digital (9, 90)-sequence over F25, using
(108, 108+∞, 170)-Net over F5 — Digital
Digital (108, m, 170)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (108, 169)-sequence over F5, using
- t-expansion [i] based on digital (103, 169)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 103 and N(F) ≥ 170, using
- t-expansion [i] based on digital (103, 169)-sequence over F5, using
(108, 108+∞, 450)-Net in Base 5 — Upper bound on s
There is no (108, m, 451)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (108, 1799, 451)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51799, 451, S5, 4, 1691), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 245655 102922 646622 231535 181459 914264 136446 542412 506662 161312 624076 936729 812096 448997 615292 883703 408940 280190 553460 915375 173739 585333 245421 748498 899760 173453 816034 700386 431985 729431 196412 495180 884634 868686 741669 666855 455121 998014 892921 239590 929282 889262 837784 634098 051977 649435 477798 549770 548838 058211 834451 959014 498972 198915 576554 602302 770186 965940 401241 009314 885703 614373 453830 711856 480816 382852 044761 559843 972737 695012 444207 727032 499246 363227 134804 253325 068022 203717 502216 272738 079027 472225 588416 540070 723427 391239 422677 216729 091337 041369 291571 272582 620296 171507 207428 661129 180694 703762 582392 373830 611974 459611 516059 612216 054185 345087 484464 809936 752113 683795 767622 991841 053780 979095 611123 638697 857733 654469 265621 181892 075343 291808 845452 355440 443259 446740 383099 187448 981935 294055 284449 010006 542277 143360 440663 917720 783706 481100 060935 407135 005899 780250 853920 384156 766811 223831 741113 434428 624664 864507 941954 662001 519189 793161 710477 397354 961864 231494 883618 580921 132203 329951 515527 141865 409861 505152 123143 411394 988888 727120 915930 596081 685876 923403 116346 409170 048970 800937 546479 813156 353364 209020 061735 014492 837792 141884 853613 024228 280347 402789 147938 826101 708215 228377 000721 375822 266825 563930 585844 531573 017967 963069 616379 491455 493422 336076 037026 941776 275634 765625 / 423 > 51799 [i]
- extracting embedded OOA [i] would yield OOA(51799, 451, S5, 4, 1691), but