Best Known (193, 193+49, s)-Nets in Base 2
(193, 193+49, 260)-Net over F2 — Constructive and digital
Digital (193, 242, 260)-net over F2, using
- t-expansion [i] based on digital (192, 242, 260)-net over F2, using
- 6 times m-reduction [i] based on digital (192, 248, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 62, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 62, 65)-net over F16, using
- 6 times m-reduction [i] based on digital (192, 248, 260)-net over F2, using
(193, 193+49, 586)-Net over F2 — Digital
Digital (193, 242, 586)-net over F2, using
(193, 193+49, 10297)-Net in Base 2 — Upper bound on s
There is no (193, 242, 10298)-net in base 2, because
- 1 times m-reduction [i] would yield (193, 241, 10298)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3 541415 428353 609802 166503 055896 948033 905578 347261 841171 344314 332677 871939 > 2241 [i]