Best Known (237−115, 237, s)-Nets in Base 4
(237−115, 237, 130)-Net over F4 — Constructive and digital
Digital (122, 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
(237−115, 237, 184)-Net over F4 — Digital
Digital (122, 237, 184)-net over F4, using
(237−115, 237, 2242)-Net in Base 4 — Upper bound on s
There is no (122, 237, 2243)-net in base 4, because
- 1 times m-reduction [i] would yield (122, 236, 2243)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12440 735153 319330 260978 364194 459809 065359 461448 948021 834296 784978 631454 725829 842066 570943 223236 073796 818955 573328 911008 375392 573472 640617 919184 > 4236 [i]