Best Known (189−84, 189, s)-Nets in Base 2
(189−84, 189, 56)-Net over F2 — Constructive and digital
Digital (105, 189, 56)-net over F2, using
- net from sequence [i] based on digital (105, 55)-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 7 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]
(189−84, 189, 69)-Net over F2 — Digital
Digital (105, 189, 69)-net over F2, using
(189−84, 189, 291)-Net in Base 2 — Upper bound on s
There is no (105, 189, 292)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2189, 292, S2, 84), but
- 7 times code embedding in larger space [i] would yield OA(2196, 299, S2, 84), but
- adding a parity check bit [i] would yield OA(2197, 300, S2, 85), but
- the linear programming bound shows that M ≥ 333445 596634 842101 957662 761369 966680 970228 955880 375209 681209 067512 159971 176505 925710 036206 046927 475988 200870 117376 / 1 055603 696799 631985 996897 950925 994087 362055 971326 408581 > 2197 [i]
- adding a parity check bit [i] would yield OA(2197, 300, S2, 85), but
- 7 times code embedding in larger space [i] would yield OA(2196, 299, S2, 84), but