Best Known (88, 88+∞, s)-Nets in Base 5
(88, 88+∞, 82)-Net over F5 — Constructive and digital
Digital (88, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (88, 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
(88, 88+∞, 150)-Net over F5 — Digital
Digital (88, m, 150)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (88, 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
(88, 88+∞, 370)-Net in Base 5 — Upper bound on s
There is no (88, m, 371)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (88, 1479, 371)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51479, 371, S5, 4, 1391), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 14050 904280 939382 743005 017532 113194 070417 922939 548595 268763 990528 367997 821388 295066 010260 751150 314228 502464 291121 916982 157348 838608 026863 544310 000756 626662 279234 905706 039202 512581 206697 475067 044552 928494 119879 866208 851690 299004 662152 535029 963530 213588 682859 143198 432256 212992 795802 651163 519590 039096 873934 137739 372430 891771 465122 769003 703826 821895 851228 522754 703645 319109 799570 339440 401727 547433 811355 741717 386773 242075 378955 735778 408412 593259 097590 727359 495817 521445 209382 293093 023920 606174 964805 171459 409965 305953 585472 946811 763821 373760 150080 367303 711067 999903 073346 166373 636865 755232 461721 385836 354125 672891 949413 267096 065869 036578 638769 665240 136341 168130 021366 315472 037953 689778 722857 306949 870431 396275 718127 498078 871689 909511 619664 260728 105673 567037 057940 285413 216027 694457 315303 484409 350411 111722 455284 274203 676816 633482 015091 944278 527522 615174 338674 409851 733972 318757 645380 215801 175163 707887 576639 268740 765610 178230 815098 333913 980385 356234 952021 329516 304231 136698 318647 769631 756986 639741 467681 741227 124803 117476 403713 226318 359375 / 174 > 51479 [i]
- extracting embedded OOA [i] would yield OOA(51479, 371, S5, 4, 1391), but