Best Known (101, 101+79, s)-Nets in Base 2
(101, 101+79, 55)-Net over F2 — Constructive and digital
Digital (101, 180, 55)-net over F2, using
- t-expansion [i] based on digital (100, 180, 55)-net over F2, using
- net from sequence [i] based on digital (100, 54)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 6 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (100, 54)-sequence over F2, using
(101, 101+79, 68)-Net over F2 — Digital
Digital (101, 180, 68)-net over F2, using
(101, 101+79, 293)-Net in Base 2 — Upper bound on s
There is no (101, 180, 294)-net in base 2, because
- 1 times m-reduction [i] would yield (101, 179, 294)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2179, 294, S2, 78), but
- 5 times code embedding in larger space [i] would yield OA(2184, 299, S2, 78), but
- adding a parity check bit [i] would yield OA(2185, 300, S2, 79), but
- the linear programming bound shows that M ≥ 141567 108182 629161 298008 913795 645564 742059 458353 673336 771152 211645 355218 507110 019263 646714 332578 792395 869231 595182 307914 419827 387939 160064 / 1898 352509 614315 308497 056354 652811 989510 912931 797163 098992 061786 535651 328793 485695 > 2185 [i]
- adding a parity check bit [i] would yield OA(2185, 300, S2, 79), but
- 5 times code embedding in larger space [i] would yield OA(2184, 299, S2, 78), but
- extracting embedded orthogonal array [i] would yield OA(2179, 294, S2, 78), but