Best Known (13, ∞, s)-Nets in Base 25
(13, ∞, 126)-Net over F25 — Constructive and digital
Digital (13, m, 126)-net over F25 for arbitrarily large m, using
- net from sequence [i] based on digital (13, 125)-sequence over F25, using
- t-expansion [i] 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
- t-expansion [i] based on digital (10, 125)-sequence over F25, using
(13, ∞, 361)-Net in Base 25 — Upper bound on s
There is no (13, m, 362)-net in base 25 for arbitrarily large m, because
- m-reduction [i] would yield (13, 721, 362)-net in base 25, but
- extracting embedded OOA [i] would yield OOA(25721, 362, S25, 2, 708), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 760 130196 267866 780073 679303 278404 608406 538111 615846 080761 539328 506004 937241 495535 370673 209084 272605 170055 333403 822602 119535 205158 041575 848324 713431 493286 972434 102936 727162 582455 121878 626467 544876 664341 944184 597843 808449 387334 870793 523974 786705 180113 238346 894374 481141 453458 037149 096760 593797 629450 278159 029579 096805 652096 887371 474725 905431 913393 477792 867985 086715 748850 969429 973018 444711 950287 941724 054172 468413 763177 607087 633224 372972 151732 741394 262439 785469 936417 179662 724896 766945 945777 434168 922556 563070 815484 566977 671199 395099 231463 002067 846633 402876 340505 254724 797253 747940 233174 683665 335894 176928 467292 106181 941016 832777 708131 131372 314098 955023 714122 221117 287465 181823 694307 880624 171880 136204 094816 471675 094872 667608 258532 564226 120729 228101 307946 078507 752364 226294 927604 018600 431576 701691 239548 292447 307868 341062 027092 827478 022443 249433 502202 125815 818102 909280 660441 067182 143222 810002 165186 199094 360188 849329 605286 292777 365237 729850 891829 357569 047951 175403 692318 684190 087907 381894 183345 139026 641845 703125 / 709 > 25721 [i]
- extracting embedded OOA [i] would yield OOA(25721, 362, S25, 2, 708), but