Best Known (124, 124+90, s)-Nets in Base 4
(124, 124+90, 130)-Net over F4 — Constructive and digital
Digital (124, 214, 130)-net over F4, using
- t-expansion [i] based on digital (105, 214, 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
(124, 124+90, 264)-Net over F4 — Digital
Digital (124, 214, 264)-net over F4, using
(124, 124+90, 4250)-Net in Base 4 — Upper bound on s
There is no (124, 214, 4251)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 697 517013 747473 714412 052162 200936 970743 363107 073233 715324 004352 696544 024845 941300 972516 193139 241038 387341 005385 006561 920687 348384 > 4214 [i]