Best Known (125, 125+88, s)-Nets in Base 4
(125, 125+88, 130)-Net over F4 — Constructive and digital
Digital (125, 213, 130)-net over F4, using
- t-expansion [i] based on digital (105, 213, 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+88, 278)-Net over F4 — Digital
Digital (125, 213, 278)-net over F4, using
(125, 125+88, 4688)-Net in Base 4 — Upper bound on s
There is no (125, 213, 4689)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 174 848759 463699 884396 021409 731301 412339 384709 058564 478693 328531 402868 518012 873222 900802 566319 135543 471926 309056 787559 157874 533480 > 4213 [i]