Best Known (82, 82+28, s)-Nets in Base 7
(82, 82+28, 688)-Net over F7 — Constructive and digital
Digital (82, 110, 688)-net over F7, using
- t-expansion [i] based on digital (76, 110, 688)-net over F7, using
- trace code for nets [i] based on digital (21, 55, 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, 55, 344)-net over F49, using
(82, 82+28, 5063)-Net over F7 — Digital
Digital (82, 110, 5063)-net over F7, using
(82, 82+28, 4399077)-Net in Base 7 — Upper bound on s
There is no (82, 110, 4399078)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 913 660053 504501 204331 821407 410325 494462 806680 352729 537153 866360 602809 931655 718263 620877 458261 > 7110 [i]