Best Known (254−115, 254, s)-Nets in Base 4
(254−115, 254, 130)-Net over F4 — Constructive and digital
Digital (139, 254, 130)-net over F4, using
- t-expansion [i] based on digital (105, 254, 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
(254−115, 254, 243)-Net over F4 — Digital
Digital (139, 254, 243)-net over F4, using
(254−115, 254, 3414)-Net in Base 4 — Upper bound on s
There is no (139, 254, 3415)-net in base 4, because
- 1 times m-reduction [i] would yield (139, 253, 3415)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 212 852400 143358 269690 127377 169701 062018 842936 065301 224712 882172 294045 996529 011512 968360 537675 583598 685993 053922 864132 494974 597822 093878 307272 796974 896720 > 4253 [i]