Best Known (258−155, 258, s)-Nets in Base 4
(258−155, 258, 104)-Net over F4 — Constructive and digital
Digital (103, 258, 104)-net over F4, using
- t-expansion [i] based on digital (73, 258, 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
(258−155, 258, 144)-Net over F4 — Digital
Digital (103, 258, 144)-net over F4, using
- t-expansion [i] based on digital (91, 258, 144)-net over F4, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 91 and N(F) ≥ 144, using
- net from sequence [i] based on digital (91, 143)-sequence over F4, using
(258−155, 258, 942)-Net in Base 4 — Upper bound on s
There is no (103, 258, 943)-net in base 4, because
- 1 times m-reduction [i] would yield (103, 257, 943)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 56120 439254 644246 685141 477747 037073 757494 594500 683052 347810 029646 032525 292158 131241 878641 013566 117235 309478 702429 942008 278805 571325 105214 259103 541537 773380 > 4257 [i]