Best Known (33, s)-Sequences in Base 7
(33, 34)-Sequence over F7 — Constructive and digital
Digital (33, 34)-sequence over F7, using
(33, 95)-Sequence over F7 — Digital
Digital (33, 95)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 33 and N(F) ≥ 96, using
(33, 217)-Sequence in Base 7 — Upper bound on s
There is no (33, 218)-sequence in base 7, because
- net from sequence [i] would yield (33, m, 219)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (33, 653, 219)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7653, 219, S7, 3, 620), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 24 722260 235775 915446 364606 453735 573696 236202 931327 884373 798232 331579 014322 258351 781696 369374 111269 666212 441894 907197 501443 902282 562925 594681 190213 376879 814848 373449 494433 366113 499905 040357 756241 333049 501706 270376 915773 991335 236865 480367 616708 008394 681149 211197 576577 407324 824227 273281 594744 030680 598536 990719 077231 926076 008539 409432 159960 861769 810219 167657 256954 205680 226606 003752 183623 057628 827680 150808 282381 419579 144429 666717 776273 594525 409151 260744 826813 493398 817403 952579 378338 524095 309143 761769 152429 946259 223496 297401 654007 183062 039248 591849 444245 / 23 > 7653 [i]
- extracting embedded OOA [i] would yield OOA(7653, 219, S7, 3, 620), but
- m-reduction [i] would yield (33, 653, 219)-net in base 7, but