Best Known (69, 93, s)-Nets in Base 7
(69, 93, 688)-Net over F7 — Constructive and digital
Digital (69, 93, 688)-net over F7, using
- 3 times m-reduction [i] based on digital (69, 96, 688)-net over F7, using
- trace code for nets [i] based on digital (21, 48, 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, 48, 344)-net over F49, using
(69, 93, 4118)-Net over F7 — Digital
Digital (69, 93, 4118)-net over F7, using
(69, 93, 3124056)-Net in Base 7 — Upper bound on s
There is no (69, 93, 3124057)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 3 927515 813695 612133 706041 066277 823645 658686 315888 249590 468074 832357 643267 877089 > 793 [i]