Best Known (193−101, 193, s)-Nets in Base 2
(193−101, 193, 53)-Net over F2 — Constructive and digital
Digital (92, 193, 53)-net over F2, using
- t-expansion [i] based on digital (90, 193, 53)-net over F2, using
- net from sequence [i] based on digital (90, 52)-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 4 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 (90, 52)-sequence over F2, using
(193−101, 193, 60)-Net over F2 — Digital
Digital (92, 193, 60)-net over F2, using
- net from sequence [i] based on digital (92, 59)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 92 and N(F) ≥ 60, using
(193−101, 193, 193)-Net over F2 — Upper bound on s (digital)
There is no digital (92, 193, 194)-net over F2, because
- 5 times m-reduction [i] would yield digital (92, 188, 194)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2188, 194, F2, 96) (dual of [194, 6, 97]-code), but
(193−101, 193, 196)-Net in Base 2 — Upper bound on s
There is no (92, 193, 197)-net in base 2, because
- 3 times m-reduction [i] would yield (92, 190, 197)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2190, 197, S2, 98), but
- adding a parity check bit [i] would yield OA(2191, 198, S2, 99), but
- the (dual) Plotkin bound shows that M ≥ 100433 627766 186892 221372 630771 322662 657637 687111 424552 206336 / 25 > 2191 [i]
- adding a parity check bit [i] would yield OA(2191, 198, S2, 99), but
- extracting embedded orthogonal array [i] would yield OA(2190, 197, S2, 98), but