Best Known (40, 81, s)-Nets in Base 7
(40, 81, 50)-Net over F7 — Constructive and digital
Digital (40, 81, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(40,49) in PG(80,7)) for nets [i] based on digital (0, 41, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
(40, 81, 122)-Net over F7 — Digital
Digital (40, 81, 122)-net over F7, using
(40, 81, 3310)-Net in Base 7 — Upper bound on s
There is no (40, 81, 3311)-net in base 7, because
- 1 times m-reduction [i] would yield (40, 80, 3311)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 40 704565 290470 338663 819348 756295 034545 176013 088127 126969 651413 619849 > 780 [i]