Best Known (235, s)-Sequences in Base 2
(235, 89)-Sequence over F2 — Constructive and digital
Digital (235, 89)-sequence over F2, using
- base reduction for sequences [i] based on digital (73, 89)-sequence over F4, using
- s-reduction 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
- s-reduction based on digital (73, 103)-sequence over F4, using
(235, 128)-Sequence over F2 — Digital
Digital (235, 128)-sequence over F2, using
- t-expansion [i] based on digital (215, 128)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 215 and N(F) ≥ 129, using
(235, 245)-Sequence in Base 2 — Upper bound on s
There is no (235, 246)-sequence in base 2, because
- net from sequence [i] would yield (235, m, 247)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (235, 1965, 247)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21965, 247, S2, 8, 1730), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 7 083980 232655 942647 757492 920199 542440 611733 846680 825299 736469 175173 623004 671608 404536 143966 807847 878159 679952 760498 915681 696648 817246 539118 417347 999852 222719 432191 719186 435034 541070 106039 664682 682758 581910 008530 800027 795570 505065 015991 919650 864690 496188 081821 406501 271848 177268 516779 315454 671978 676258 158068 220308 255609 475072 620102 081936 138125 310585 781143 439402 786841 579966 324417 628956 619258 210060 437922 307460 983295 646417 134362 849656 299771 995647 265188 326124 114533 641157 628188 669469 761061 882288 755640 487693 206588 664882 377491 432335 495365 421488 543060 312256 140515 770561 112569 024382 801923 259855 011840 / 1731 > 21965 [i]
- extracting embedded OOA [i] would yield OOA(21965, 247, S2, 8, 1730), but
- m-reduction [i] would yield (235, 1965, 247)-net in base 2, but