Best Known (237−110, 237, s)-Nets in Base 4
(237−110, 237, 130)-Net over F4 — Constructive and digital
Digital (127, 237, 130)-net over F4, using
- t-expansion [i] based on digital (105, 237, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(237−110, 237, 211)-Net over F4 — Digital
Digital (127, 237, 211)-net over F4, using
(237−110, 237, 2749)-Net in Base 4 — Upper bound on s
There is no (127, 237, 2750)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 48916 383152 742247 670552 310967 045610 764058 467555 683016 556899 323656 360425 225808 676966 229072 308636 343813 043943 603818 226637 551627 261690 293536 582756 > 4237 [i]