Best Known (227−100, 227, s)-Nets in Base 4
(227−100, 227, 130)-Net over F4 — Constructive and digital
Digital (127, 227, 130)-net over F4, using
- t-expansion [i] based on digital (105, 227, 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
(227−100, 227, 239)-Net over F4 — Digital
Digital (127, 227, 239)-net over F4, using
(227−100, 227, 3473)-Net in Base 4 — Upper bound on s
There is no (127, 227, 3474)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 46682 192331 032345 120396 390726 059061 020808 132971 277162 690596 090924 332019 826264 762461 356108 516649 641846 585280 988997 536867 683576 517960 404000 > 4227 [i]