Best Known (113, 113+102, s)-Nets in Base 4
(113, 113+102, 130)-Net over F4 — Constructive and digital
Digital (113, 215, 130)-net over F4, using
- t-expansion [i] based on digital (105, 215, 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
(113, 113+102, 181)-Net over F4 — Digital
Digital (113, 215, 181)-net over F4, using
(113, 113+102, 2242)-Net in Base 4 — Upper bound on s
There is no (113, 215, 2243)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2772 678677 541227 215811 095010 449247 312686 612987 026987 214558 946827 879583 761571 813150 539538 563749 003282 877231 581473 635334 434761 552880 > 4215 [i]