Best Known (125, 125+108, s)-Nets in Base 4
(125, 125+108, 130)-Net over F4 — Constructive and digital
Digital (125, 233, 130)-net over F4, using
- t-expansion [i] based on digital (105, 233, 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
(125, 125+108, 209)-Net over F4 — Digital
Digital (125, 233, 209)-net over F4, using
(125, 125+108, 2723)-Net in Base 4 — Upper bound on s
There is no (125, 233, 2724)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 190 605860 223368 054870 303008 891009 858488 165245 017368 134190 197260 566877 139785 671664 683030 528150 366775 407679 428980 158865 297163 884502 581279 900320 > 4233 [i]