Best Known (80, 80+55, s)-Nets in Base 2
(80, 80+55, 56)-Net over F2 — Constructive and digital
Digital (80, 135, 56)-net over F2, using
- 1 times m-reduction [i] based on digital (80, 136, 56)-net over F2, using
- trace code for nets [i] based on digital (12, 68, 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
- trace code for nets [i] based on digital (12, 68, 28)-net over F4, using
(80, 80+55, 64)-Net over F2 — Digital
Digital (80, 135, 64)-net over F2, using
(80, 80+55, 298)-Net in Base 2 — Upper bound on s
There is no (80, 135, 299)-net in base 2, because
- 1 times m-reduction [i] would yield (80, 134, 299)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2134, 299, S2, 54), but
- adding a parity check bit [i] would yield OA(2135, 300, S2, 55), but
- the linear programming bound shows that M ≥ 48 453210 492851 688423 719096 496218 730424 623843 475355 389039 083584 741794 713780 743579 191978 463824 301856 084801 540325 376000 / 597 625262 017249 457875 009714 443330 928540 125079 140107 131223 189140 092691 487281 > 2135 [i]
- adding a parity check bit [i] would yield OA(2135, 300, S2, 55), but
- extracting embedded orthogonal array [i] would yield OA(2134, 299, S2, 54), but