Best Known (80, 80+58, s)-Nets in Base 4
(80, 80+58, 130)-Net over F4 — Constructive and digital
Digital (80, 138, 130)-net over F4, using
- 10 times m-reduction [i] based on digital (80, 148, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 74, 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
- trace code for nets [i] based on digital (6, 74, 65)-net over F16, using
(80, 80+58, 181)-Net over F4 — Digital
Digital (80, 138, 181)-net over F4, using
(80, 80+58, 2827)-Net in Base 4 — Upper bound on s
There is no (80, 138, 2828)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 122323 346960 964739 703145 718383 777781 256229 312229 189272 375170 633860 230392 480265 715648 > 4138 [i]