Best Known (161, 161+95, s)-Nets in Base 4
(161, 161+95, 200)-Net over F4 — Constructive and digital
Digital (161, 256, 200)-net over F4, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the 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) = 161 and N(F) ≥ 200, using
(161, 161+95, 468)-Net over F4 — Digital
Digital (161, 256, 468)-net over F4, using
(161, 161+95, 11271)-Net in Base 4 — Upper bound on s
There is no (161, 256, 11272)-net in base 4, because
- 1 times m-reduction [i] would yield (161, 255, 11272)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3356 493601 596944 834987 879647 464157 635685 160810 052881 174335 934603 617039 694007 355232 998648 257015 991177 597714 902223 042784 063475 802639 392535 841146 051116 365440 > 4255 [i]