Best Known (260−165, 260, s)-Nets in Base 2
(260−165, 260, 54)-Net over F2 — Constructive and digital
Digital (95, 260, 54)-net over F2, using
- net from sequence [i] based on digital (95, 53)-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 5 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]
(260−165, 260, 65)-Net over F2 — Digital
Digital (95, 260, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
(260−165, 260, 177)-Net in Base 2 — Upper bound on s
There is no (95, 260, 178)-net in base 2, because
- 1 times m-reduction [i] would yield (95, 259, 178)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 152560 267781 356027 845362 074118 754302 458692 234839 378692 866161 143633 933800 708688 > 2259 [i]