Best Known (91, 180, s)-Nets in Base 2
(91, 180, 53)-Net over F2 — Constructive and digital
Digital (91, 180, 53)-net over F2, using
- t-expansion [i] based on digital (90, 180, 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
(91, 180, 57)-Net over F2 — Digital
Digital (91, 180, 57)-net over F2, using
- t-expansion [i] based on digital (83, 180, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(91, 180, 199)-Net over F2 — Upper bound on s (digital)
There is no digital (91, 180, 200)-net over F2, because
- 1 times m-reduction [i] would yield digital (91, 179, 200)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2179, 200, F2, 88) (dual of [200, 21, 89]-code), but
- residual code [i] would yield OA(291, 111, S2, 44), but
- the linear programming bound shows that M ≥ 4098 314390 537865 655038 841462 980608 / 1 584999 > 291 [i]
- residual code [i] would yield OA(291, 111, S2, 44), but
- extracting embedded orthogonal array [i] would yield linear OA(2179, 200, F2, 88) (dual of [200, 21, 89]-code), but
(91, 180, 229)-Net in Base 2 — Upper bound on s
There is no (91, 180, 230)-net in base 2, because
- 1 times m-reduction [i] would yield (91, 179, 230)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 767945 292862 876955 714737 034659 525318 005667 882476 666888 > 2179 [i]