Best Known (114, 114+72, s)-Nets in Base 4
(114, 114+72, 130)-Net over F4 — Constructive and digital
Digital (114, 186, 130)-net over F4, using
- t-expansion [i] based on digital (105, 186, 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
(114, 114+72, 306)-Net over F4 — Digital
Digital (114, 186, 306)-net over F4, using
(114, 114+72, 6111)-Net in Base 4 — Upper bound on s
There is no (114, 186, 6112)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 9628 804453 820320 358562 197407 209020 839586 698331 704499 069191 867599 003692 894958 286881 133634 115244 964929 819411 079446 > 4186 [i]