Best Known (38, 77, s)-Nets in Base 7
(38, 77, 50)-Net over F7 — Constructive and digital
Digital (38, 77, 50)-net over F7, using
- base reduction for projective spaces (embedding PG(38,49) in PG(76,7)) for nets [i] based on digital (0, 39, 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
(38, 77, 117)-Net over F7 — Digital
Digital (38, 77, 117)-net over F7, using
(38, 77, 3160)-Net in Base 7 — Upper bound on s
There is no (38, 77, 3161)-net in base 7, because
- 1 times m-reduction [i] would yield (38, 76, 3161)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 16908 475223 263791 659100 498271 479333 681633 769964 318039 275251 656023 > 776 [i]