Best Known (104, 104+99, s)-Nets in Base 2
(104, 104+99, 55)-Net over F2 — Constructive and digital
Digital (104, 203, 55)-net over F2, using
- t-expansion [i] based on digital (100, 203, 55)-net over F2, using
- net from sequence [i] based on digital (100, 54)-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 6 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 (100, 54)-sequence over F2, using
(104, 104+99, 65)-Net over F2 — Digital
Digital (104, 203, 65)-net over F2, using
- t-expansion [i] based on digital (95, 203, 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
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(104, 104+99, 233)-Net over F2 — Upper bound on s (digital)
There is no digital (104, 203, 234)-net over F2, because
- 1 times m-reduction [i] would yield digital (104, 202, 234)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2202, 234, F2, 98) (dual of [234, 32, 99]-code), but
- residual code [i] would yield OA(2104, 135, S2, 49), but
- 1 times truncation [i] would yield OA(2103, 134, S2, 48), but
- the linear programming bound shows that M ≥ 14817 140394 002966 911489 108655 371959 926784 / 1391 278625 > 2103 [i]
- 1 times truncation [i] would yield OA(2103, 134, S2, 48), but
- residual code [i] would yield OA(2104, 135, S2, 49), but
- extracting embedded orthogonal array [i] would yield linear OA(2202, 234, F2, 98) (dual of [234, 32, 99]-code), but
(104, 104+99, 266)-Net in Base 2 — Upper bound on s
There is no (104, 203, 267)-net in base 2, because
- 1 times m-reduction [i] would yield (104, 202, 267)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 7 002752 860830 517919 539481 172668 989636 712529 615994 155226 304832 > 2202 [i]