Best Known (129, 129+121, s)-Nets in Base 4
(129, 129+121, 130)-Net over F4 — Constructive and digital
Digital (129, 250, 130)-net over F4, using
- t-expansion [i] based on digital (105, 250, 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
(129, 129+121, 194)-Net over F4 — Digital
Digital (129, 250, 194)-net over F4, using
(129, 129+121, 2387)-Net in Base 4 — Upper bound on s
There is no (129, 250, 2388)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 249, 2388)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 831215 932859 263550 511398 506928 013468 760780 901514 674855 597186 347956 861603 072892 621556 375335 229387 049045 049110 787889 743612 092922 197806 893125 982331 367568 > 4249 [i]