Best Known (100−26, 100, s)-Nets in Base 7
(100−26, 100, 688)-Net over F7 — Constructive and digital
Digital (74, 100, 688)-net over F7, using
- 6 times m-reduction [i] based on digital (74, 106, 688)-net over F7, using
- trace code for nets [i] based on digital (21, 53, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- trace code for nets [i] based on digital (21, 53, 344)-net over F49, using
(100−26, 100, 4085)-Net over F7 — Digital
Digital (74, 100, 4085)-net over F7, using
(100−26, 100, 2992319)-Net in Base 7 — Upper bound on s
There is no (74, 100, 2992320)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 3 234489 951898 277520 555935 345528 296046 792687 747659 630957 829949 739399 946929 311310 105729 > 7100 [i]