Best Known (232−106, 232, s)-Nets in Base 4
(232−106, 232, 130)-Net over F4 — Constructive and digital
Digital (126, 232, 130)-net over F4, using
- t-expansion [i] based on digital (105, 232, 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
(232−106, 232, 218)-Net over F4 — Digital
Digital (126, 232, 218)-net over F4, using
(232−106, 232, 2922)-Net in Base 4 — Upper bound on s
There is no (126, 232, 2923)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 48 400875 890876 803638 502402 231076 670294 122075 814138 860822 539597 822946 746960 218763 197587 110984 504528 041076 599743 146006 811978 747797 563166 282000 > 4232 [i]