Best Known (83, s)-Sequences in Base 3
(83, 57)-Sequence over F3 — Constructive and digital
Digital (83, 57)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 57)-sequence over F9, using
- s-reduction based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- s-reduction based on digital (13, 63)-sequence over F9, using
(83, 83)-Sequence over F3 — Digital
Digital (83, 83)-sequence over F3, using
- t-expansion [i] based on digital (71, 83)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 71 and N(F) ≥ 84, using
(83, 177)-Sequence in Base 3 — Upper bound on s
There is no (83, 178)-sequence in base 3, because
- net from sequence [i] would yield (83, m, 179)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (83, 889, 179)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3889, 179, S3, 5, 806), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 982246 503426 804619 573497 761743 551171 028766 478635 603845 973220 199973 440768 572333 167972 922227 199274 310217 758679 793786 270612 763681 969476 148245 047736 708812 167104 858671 644941 931640 753887 193924 001956 157724 091375 688897 563031 474050 518479 891747 453641 302611 794934 290630 891278 389850 892690 500289 184436 078584 703044 582720 371644 101405 261905 805849 083631 646533 836446 956471 683405 432868 706002 758276 040327 991125 745741 253654 858912 115161 082114 332825 / 269 > 3889 [i]
- extracting embedded OOA [i] would yield OOA(3889, 179, S3, 5, 806), but
- m-reduction [i] would yield (83, 889, 179)-net in base 3, but