Best Known (94−80, 94, s)-Nets in Base 16
(94−80, 94, 65)-Net over F16 — Constructive and digital
Digital (14, 94, 65)-net over F16, using
- t-expansion [i] based on digital (6, 94, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(94−80, 94, 97)-Net over F16 — Digital
Digital (14, 94, 97)-net over F16, using
- t-expansion [i] based on digital (13, 94, 97)-net over F16, using
- net from sequence [i] based on digital (13, 96)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 13 and N(F) ≥ 97, using
- net from sequence [i] based on digital (13, 96)-sequence over F16, using
(94−80, 94, 688)-Net in Base 16 — Upper bound on s
There is no (14, 94, 689)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 160954 576883 994678 319075 550360 439824 464086 925686 330691 661374 360011 678249 367350 748501 405070 399520 799946 650726 394026 > 1694 [i]