Best Known (234−102, 234, s)-Nets in Base 4
(234−102, 234, 130)-Net over F4 — Constructive and digital
Digital (132, 234, 130)-net over F4, using
- t-expansion [i] based on digital (105, 234, 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
(234−102, 234, 254)-Net over F4 — Digital
Digital (132, 234, 254)-net over F4, using
(234−102, 234, 3787)-Net in Base 4 — Upper bound on s
There is no (132, 234, 3788)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 766 766552 969437 294279 400762 366017 389262 967073 278074 426433 142996 752709 609262 739728 412733 436548 374459 610913 394547 431332 227362 591342 895264 613300 > 4234 [i]