Best Known (178−73, 178, s)-Nets in Base 4
(178−73, 178, 130)-Net over F4 — Constructive and digital
Digital (105, 178, 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
(178−73, 178, 243)-Net over F4 — Digital
Digital (105, 178, 243)-net over F4, using
(178−73, 178, 4313)-Net in Base 4 — Upper bound on s
There is no (105, 178, 4314)-net in base 4, because
- 1 times m-reduction [i] would yield (105, 177, 4314)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 36964 768373 166134 692237 379590 318537 150180 822146 657389 157365 732013 950435 236225 454747 018732 643736 153296 509020 > 4177 [i]