Best Known (126, 126+42, s)-Nets in Base 4
(126, 126+42, 1028)-Net over F4 — Constructive and digital
Digital (126, 168, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 42, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
(126, 126+42, 1597)-Net over F4 — Digital
Digital (126, 168, 1597)-net over F4, using
(126, 126+42, 189588)-Net in Base 4 — Upper bound on s
There is no (126, 168, 189589)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 139989 676867 309103 024129 188751 594098 126838 403013 301710 347896 399472 801748 956695 882567 053410 505000 391668 > 4168 [i]