Best Known (181−68, 181, s)-Nets in Base 4
(181−68, 181, 130)-Net over F4 — Constructive and digital
Digital (113, 181, 130)-net over F4, using
- t-expansion [i] based on digital (105, 181, 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
(181−68, 181, 332)-Net over F4 — Digital
Digital (113, 181, 332)-net over F4, using
(181−68, 181, 7207)-Net in Base 4 — Upper bound on s
There is no (113, 181, 7208)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 9 429424 915111 646989 997618 372721 093953 688161 876871 963694 822152 583319 151868 523563 507610 631574 663479 989238 659341 > 4181 [i]