Best Known (2, s)-Sequences in Base 81
(2, 115)-Sequence over F81 — Constructive and digital
Digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
(2, 117)-Sequence over F81 — Digital
Digital (2, 117)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 118, using
(2, 245)-Sequence in Base 81 — Upper bound on s
There is no (2, 246)-sequence in base 81, because
- net from sequence [i] would yield (2, m, 247)-net in base 81 for arbitrarily large m, but
- m-reduction [i] would yield (2, 245, 247)-net in base 81, but
- extracting embedded OOA [i] would yield OA(81245, 247, S81, 243), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 30 712462 848931 202840 988870 203427 210308 664904 645167 936662 700054 859621 679368 951351 707851 994437 639235 331395 154992 104336 642875 794292 952083 827984 606370 488891 678277 367984 084044 887039 782072 465611 604685 857266 575951 014202 478487 218936 445692 067034 935670 340295 477802 041603 249649 245189 826523 535646 206768 347541 614520 098309 700954 081463 772588 588487 339323 427141 374052 720180 450854 999460 752698 129084 877231 805066 382189 438054 072134 545891 169366 949328 158715 009841 651632 667082 032384 606083 443681 / 61 > 81245 [i]
- extracting embedded OOA [i] would yield OA(81245, 247, S81, 243), but
- m-reduction [i] would yield (2, 245, 247)-net in base 81, but