Best Known (239−105, 239, s)-Nets in Base 4
(239−105, 239, 130)-Net over F4 — Constructive and digital
Digital (134, 239, 130)-net over F4, using
- t-expansion [i] based on digital (105, 239, 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
(239−105, 239, 253)-Net over F4 — Digital
Digital (134, 239, 253)-net over F4, using
(239−105, 239, 3797)-Net in Base 4 — Upper bound on s
There is no (134, 239, 3798)-net in base 4, because
- 1 times m-reduction [i] would yield (134, 238, 3798)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 196206 169102 152459 765103 865685 513333 784284 933716 384340 052668 701895 505993 840562 748016 332351 073145 100705 898060 514047 940095 603605 992602 094846 859310 > 4238 [i]