Best Known (97, s)-Sequences in Base 4
(97, 103)-Sequence over F4 — Constructive and digital
Digital (97, 103)-sequence over F4, using
- t-expansion [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
(97, 143)-Sequence over F4 — Digital
Digital (97, 143)-sequence over F4, using
- t-expansion [i] based on digital (91, 143)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 91 and N(F) ≥ 144, using
(97, 306)-Sequence in Base 4 — Upper bound on s
There is no (97, 307)-sequence in base 4, because
- net from sequence [i] would yield (97, m, 308)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (97, 1227, 308)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(41227, 308, S4, 4, 1130), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2307 241773 742051 122883 546057 040447 438209 613869 162236 433232 042980 789686 998936 103493 739388 703789 197460 766892 245200 598053 890723 611645 283581 236208 532890 522534 759053 710142 674933 008029 611129 341437 972352 657808 642785 008686 213866 277510 742442 970530 425745 841322 665424 215366 023266 684322 554478 920277 131488 656825 733288 694404 971543 782950 289034 791649 741450 823131 717627 092608 303069 558835 459635 856953 741390 569773 352602 720698 873436 522793 523996 795638 372469 974680 963264 494716 723931 356573 670839 731998 449721 015508 313476 057030 338684 559641 324447 188545 662262 321798 040977 714299 763703 978073 199693 872522 219407 480813 509335 153085 053824 815741 296226 623329 846892 156236 349520 734547 082026 642255 680877 172683 071469 911882 502836 094649 205668 744066 037730 142881 882134 760050 749066 969088 / 377 > 41227 [i]
- extracting embedded OOA [i] would yield OOA(41227, 308, S4, 4, 1130), but
- m-reduction [i] would yield (97, 1227, 308)-net in base 4, but