Best Known (77, 77+175, s)-Nets in Base 4
(77, 77+175, 104)-Net over F4 — Constructive and digital
Digital (77, 252, 104)-net over F4, using
- t-expansion [i] based on digital (73, 252, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(77, 77+175, 112)-Net over F4 — Digital
Digital (77, 252, 112)-net over F4, using
- t-expansion [i] based on digital (73, 252, 112)-net over F4, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 112, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
(77, 77+175, 534)-Net in Base 4 — Upper bound on s
There is no (77, 252, 535)-net in base 4, because
- 1 times m-reduction [i] would yield (77, 251, 535)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 13 514884 578460 382935 816019 751382 493484 537167 309135 266738 937214 192091 907011 922325 523189 725083 107006 486485 807042 975152 879030 932395 187870 756159 658495 620000 > 4251 [i]