Best Known (133, 133+∞, s)-Nets in Base 5
(133, 133+∞, 114)-Net over F5 — Constructive and digital
Digital (133, m, 114)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (133, 113)-sequence over F5, using
- base reduction for sequences [i] based on digital (10, 113)-sequence over F25, using
- s-reduction 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
- s-reduction based on digital (10, 125)-sequence over F25, using
- base reduction for sequences [i] based on digital (10, 113)-sequence over F25, using
(133, 133+∞, 210)-Net over F5 — Digital
Digital (133, m, 210)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (133, 209)-sequence over F5, using
- t-expansion [i] based on digital (127, 209)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 127 and N(F) ≥ 210, using
- t-expansion [i] based on digital (127, 209)-sequence over F5, using
(133, 133+∞, 551)-Net in Base 5 — Upper bound on s
There is no (133, m, 552)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (133, 2203, 552)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52203, 552, S5, 4, 2070), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16 497514 464122 337649 667653 097332 841159 597566 002376 912392 606800 419240 780392 508464 998832 782655 047250 029188 795904 218440 641188 768806 700069 246161 295236 020127 613538 725492 791587 759743 320016 994055 643130 185834 443479 475820 693477 554657 497558 288893 698537 150563 141983 924050 033649 283443 134004 885544 383614 200179 118837 049265 062471 583792 770826 263416 099934 662527 379869 440719 310709 061164 295302 431068 817483 320417 247135 364132 197077 789621 611086 801915 496987 731691 077867 851409 583956 797127 996994 601676 286750 104020 495962 375543 685377 022998 308998 021328 488919 558998 992225 698099 431163 314808 372355 432083 921456 999705 131229 172527 478162 887544 697240 925647 736438 703977 487919 024095 266447 357679 759333 170117 607665 376425 793337 837685 933184 120077 012083 882869 356129 700825 476624 131429 126461 837238 046352 008998 398520 659145 962356 960754 657459 782902 585058 821091 209441 108878 592430 413041 098268 709885 459877 703615 908433 547290 891238 107381 462424 406840 267263 410748 596070 131932 763511 078751 565643 639734 453110 821945 564896 483006 543001 736649 512131 105242 552950 605037 025075 373102 013352 515851 736526 195499 873708 201292 858131 337814 641377 992356 134714 675020 717722 613469 027802 280870 803632 556268 647641 611592 913150 057627 368370 844635 800778 984203 752236 808319 553836 370567 558092 048355 811682 591548 576941 227389 767896 162725 691367 150740 617837 360058 072923 032046 122489 303063 395846 972609 664880 400647 296567 046607 414478 887886 750506 946018 916555 234984 260947 394054 806822 152404 752273 870835 539007 266141 861208 275704 708454 506673 044539 879738 938971 062418 421958 012490 734600 704430 753651 691932 601375 777112 107101 629590 033553 540706 634521 484375 / 2071 > 52203 [i]
- extracting embedded OOA [i] would yield OOA(52203, 552, S5, 4, 2070), but