Best Known (123, 123+96, s)-Nets in Base 4
(123, 123+96, 130)-Net over F4 — Constructive and digital
Digital (123, 219, 130)-net over F4, using
- t-expansion [i] based on digital (105, 219, 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
(123, 123+96, 236)-Net over F4 — Digital
Digital (123, 219, 236)-net over F4, using
(123, 123+96, 3448)-Net in Base 4 — Upper bound on s
There is no (123, 219, 3449)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 713761 896974 517370 939436 415782 435722 400023 710799 621600 616289 388584 725638 174676 727701 492729 594880 007644 370949 556473 342060 468656 319905 > 4219 [i]