Best Known (121, 121+88, s)-Nets in Base 4
(121, 121+88, 130)-Net over F4 — Constructive and digital
Digital (121, 209, 130)-net over F4, using
- t-expansion [i] based on digital (105, 209, 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
(121, 121+88, 258)-Net over F4 — Digital
Digital (121, 209, 258)-net over F4, using
(121, 121+88, 4128)-Net in Base 4 — Upper bound on s
There is no (121, 209, 4129)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 679221 459766 208112 462002 649767 854141 341233 337896 108177 392554 140990 272681 532656 711204 991889 370944 243203 752520 046721 586800 313344 > 4209 [i]