Best Known (241−170, 241, s)-Nets in Base 4
(241−170, 241, 66)-Net over F4 — Constructive and digital
Digital (71, 241, 66)-net over F4, using
- t-expansion [i] based on digital (49, 241, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 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) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(241−170, 241, 105)-Net over F4 — Digital
Digital (71, 241, 105)-net over F4, using
- t-expansion [i] based on digital (70, 241, 105)-net over F4, using
- net from sequence [i] based on digital (70, 104)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 70 and N(F) ≥ 105, using
- net from sequence [i] based on digital (70, 104)-sequence over F4, using
(241−170, 241, 483)-Net in Base 4 — Upper bound on s
There is no (71, 241, 484)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 12 930849 873228 740088 762533 695162 313879 499131 625387 884525 484721 138074 251245 439187 876671 003448 147091 969462 215771 557927 451973 749853 986939 656008 056760 > 4241 [i]