Best Known (96, s)-Sequences in Base 5
(96, 81)-Sequence over F5 — Constructive and digital
Digital (96, 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
(96, 154)-Sequence over F5 — Digital
Digital (96, 154)-sequence over F5, using
- t-expansion [i] based on digital (94, 154)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 94 and N(F) ≥ 155, using
(96, 401)-Sequence in Base 5 — Upper bound on s
There is no (96, 402)-sequence in base 5, because
- net from sequence [i] would yield (96, m, 403)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (96, 1607, 403)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51607, 403, S5, 4, 1511), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4041 334552 578144 935890 726960 392297 057857 533946 848923 244955 045967 787344 592103 631949 985000 393274 030490 807402 432731 673982 386472 240536 773145 649430 764987 101267 085838 497616 559568 508239 388686 954469 853326 926938 246966 961476 061185 201459 945810 874254 307213 321002 782689 353138 290221 413349 439700 335540 855418 137146 833975 859517 690228 156842 395814 415133 483682 482979 653322 082505 446671 374781 136301 785759 462122 083261 440692 777844 495899 926607 474213 322022 610797 516465 640084 389477 143539 047045 070636 409530 574997 303768 087789 746105 093474 698359 851840 849390 172340 365509 775151 523709 461280 588763 074171 532004 464732 204134 850169 626172 051808 086696 677075 018032 230923 304262 841282 695745 241773 926757 342418 536269 900740 971317 630761 965565 086405 548686 916402 839539 040088 251331 317214 562691 030146 797413 521308 070122 773143 364068 832929 494837 527647 621973 862206 801983 645387 114247 155040 763816 668045 229282 094786 326680 343997 994028 630884 008338 743937 988289 424313 676959 916550 824443 237772 105443 107125 233283 289708 482560 216383 732743 776865 117647 713774 690953 826242 302647 794858 556472 556261 639447 751601 221328 431528 461394 918378 449889 208216 097595 598127 398264 232112 978788 791224 360466 003417 968750 / 189 > 51607 [i]
- extracting embedded OOA [i] would yield OOA(51607, 403, S5, 4, 1511), but
- m-reduction [i] would yield (96, 1607, 403)-net in base 5, but