Best Known (125−91, 125, s)-Nets in Base 5
(125−91, 125, 72)-Net over F5 — Constructive and digital
Digital (34, 125, 72)-net over F5, using
- t-expansion [i] based on digital (31, 125, 72)-net over F5, using
- net from sequence [i] based on digital (31, 71)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 31 and N(F) ≥ 72, using
- net from sequence [i] based on digital (31, 71)-sequence over F5, using
(125−91, 125, 76)-Net over F5 — Digital
Digital (34, 125, 76)-net over F5, using
- net from sequence [i] based on digital (34, 75)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 34 and N(F) ≥ 76, using
(125−91, 125, 297)-Net in Base 5 — Upper bound on s
There is no (34, 125, 298)-net in base 5, because
- 1 times m-reduction [i] would yield (34, 124, 298)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5124, 298, S5, 90), but
- 2 times code embedding in larger space [i] would yield OA(5126, 300, S5, 90), but
- the linear programming bound shows that M ≥ 8 760573 217239 846422 453935 651008 911721 571354 103001 890845 302733 989611 059685 964454 401970 300008 618982 783022 134541 662585 261700 539326 848339 062515 705862 512551 428206 128222 100264 158078 137693 733007 063019 693882 314476 283506 365367 809389 915405 618233 916253 084082 224444 048222 380003 930846 047174 273202 632768 267991 836836 360547 069705 064497 241308 741118 583985 005484 867597 445129 131069 217306 490865 241384 025115 048096 301149 659587 935203 937586 409104 087485 396525 474195 167331 199494 462262 723283 919473 688674 059369 544126 324177 654486 228546 605768 651542 058743 920114 195768 977793 932208 442129 194736 480712 890625 / 726 376573 349909 890769 962978 140383 085414 746426 278869 187339 027401 586560 455943 276015 927871 333040 094371 026988 618035 543733 460177 551535 489398 952559 973885 988837 549841 462073 757903 582660 340305 738634 626554 459461 525514 255375 868698 270675 548232 169328 304175 955390 484906 784288 597447 263039 310858 615297 076654 124075 817568 540626 189090 748453 680693 410736 841068 493105 578093 741469 637018 646801 330935 941492 416550 027339 100285 544719 486196 379299 396885 318039 153371 666679 426524 017655 890202 573518 031449 659807 866827 > 5126 [i]
- 2 times code embedding in larger space [i] would yield OA(5126, 300, S5, 90), but
- extracting embedded orthogonal array [i] would yield OA(5124, 298, S5, 90), but