Best Known (105−32, 105, s)-Nets in Base 7
(105−32, 105, 344)-Net over F7 — Constructive and digital
Digital (73, 105, 344)-net over F7, using
- base reduction for projective spaces (embedding PG(52,49) in PG(104,7)) 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
(105−32, 105, 1523)-Net over F7 — Digital
Digital (73, 105, 1523)-net over F7, using
(105−32, 105, 398411)-Net in Base 7 — Upper bound on s
There is no (73, 105, 398412)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 54362 109006 361613 740823 287178 389532 116682 810291 707424 851914 497685 270069 254451 757000 487809 > 7105 [i]