Best Known (121, 121+119, s)-Nets in Base 4
(121, 121+119, 130)-Net over F4 — Constructive and digital
Digital (121, 240, 130)-net over F4, using
- t-expansion [i] based on digital (105, 240, 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+119, 173)-Net over F4 — Digital
Digital (121, 240, 173)-net over F4, using
(121, 121+119, 2041)-Net in Base 4 — Upper bound on s
There is no (121, 240, 2042)-net in base 4, because
- 1 times m-reduction [i] would yield (121, 239, 2042)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 793761 093103 571857 505790 261680 389891 242680 796814 160505 005784 410782 984703 059658 661746 678396 971465 947306 354102 411836 175502 685360 904429 854774 238160 > 4239 [i]