Best Known (33, 33+33, s)-Nets in Base 7
(33, 33+33, 100)-Net over F7 — Constructive and digital
Digital (33, 66, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 33, 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
(33, 33+33, 110)-Net over F7 — Digital
Digital (33, 66, 110)-net over F7, using
(33, 33+33, 3063)-Net in Base 7 — Upper bound on s
There is no (33, 66, 3064)-net in base 7, because
- 1 times m-reduction [i] would yield (33, 65, 3064)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 8 578552 728537 334336 107178 112066 517589 949523 504529 181185 > 765 [i]