Best Known (212−96, 212, s)-Nets in Base 4
(212−96, 212, 130)-Net over F4 — Constructive and digital
Digital (116, 212, 130)-net over F4, using
- t-expansion [i] based on digital (105, 212, 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
(212−96, 212, 207)-Net over F4 — Digital
Digital (116, 212, 207)-net over F4, using
(212−96, 212, 2810)-Net in Base 4 — Upper bound on s
There is no (116, 212, 2811)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 43 913741 095561 054804 130845 450863 695849 905257 631386 611058 190851 868911 035225 996636 278084 413470 086112 783586 848990 609497 437084 682525 > 4212 [i]