Best Known (89, 89+65, s)-Nets in Base 2
(89, 89+65, 56)-Net over F2 — Constructive and digital
Digital (89, 154, 56)-net over F2, using
- trace code for nets [i] based on digital (12, 77, 28)-net over F4, using
- net from sequence [i] based on digital (12, 27)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 12 and N(F) ≥ 28, using
- net from sequence [i] based on digital (12, 27)-sequence over F4, using
(89, 89+65, 66)-Net over F2 — Digital
Digital (89, 154, 66)-net over F2, using
(89, 89+65, 296)-Net in Base 2 — Upper bound on s
There is no (89, 154, 297)-net in base 2, because
- 1 times m-reduction [i] would yield (89, 153, 297)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2153, 297, S2, 64), but
- 2 times code embedding in larger space [i] would yield OA(2155, 299, S2, 64), but
- adding a parity check bit [i] would yield OA(2156, 300, S2, 65), but
- the linear programming bound shows that M ≥ 128607 777667 590210 101653 887173 502040 894764 406529 081359 436092 226095 435913 941987 570777 569145 470251 724943 577631 173973 297694 024156 054099 708915 942419 039694 767192 355181 796635 699236 752266 921629 034696 757646 591443 004827 364588 306066 675979 091547 788311 793826 285521 257433 775323 742208 / 945835 365322 447957 734477 024966 929879 951514 714129 159268 062881 655454 850565 852412 719643 836587 534403 867241 892993 866116 511199 774392 874816 973079 330110 925502 901663 854814 682186 110117 073759 483054 432263 314079 437236 978378 564192 941625 > 2156 [i]
- adding a parity check bit [i] would yield OA(2156, 300, S2, 65), but
- 2 times code embedding in larger space [i] would yield OA(2155, 299, S2, 64), but
- extracting embedded orthogonal array [i] would yield OA(2153, 297, S2, 64), but