Best Known (83, ∞, s)-Nets in Base 5
(83, ∞, 82)-Net over F5 — Constructive and digital
Digital (83, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (83, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(83, ∞, 150)-Net over F5 — Digital
Digital (83, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (83, 149)-sequence over F5, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 76 and N(F) ≥ 150, using
- t-expansion [i] based on digital (76, 149)-sequence over F5, using
(83, ∞, 350)-Net in Base 5 — Upper bound on s
There is no (83, m, 351)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (83, 1399, 351)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51399, 351, S5, 4, 1316), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 458 996941 216700 175404 128520 471576 685343 876310 176399 794280 674327 468960 410013 450222 149715 789941 434268 687024 281086 266277 844943 342383 938436 144665 991636 558180 138065 599354 934544 895388 916415 805865 604474 422891 029469 135236 578458 528019 054531 820374 755721 072275 653970 887191 887966 869937 651611 584794 470806 942674 912379 094941 943213 568238 740126 473883 076672 257617 389535 352580 444816 691644 038544 204655 312198 807164 142133 659536 151625 008036 340551 211902 588615 905000 343940 167284 632835 990144 613547 725228 658681 512053 412802 438277 551051 541152 474334 901064 435730 670110 064275 404491 447600 426343 654375 880668 580568 561679 145055 111234 910698 108322 873808 686001 205598 098594 901684 437898 839062 027221 426969 511483 098313 783913 346437 405687 274428 730205 144898 436718 821367 190406 208529 026547 584426 801106 623493 009408 692959 471425 993574 048765 569271 848475 345194 871336 867650 220025 841959 280775 244177 046595 062638 756106 879834 618152 591790 960961 235928 220298 729513 319088 905505 293650 872549 016014 236163 661654 810397 294568 247161 805629 730224 609375 / 439 > 51399 [i]
- extracting embedded OOA [i] would yield OOA(51399, 351, S5, 4, 1316), but