Best Known (248−143, 248, s)-Nets in Base 4
(248−143, 248, 130)-Net over F4 — Constructive and digital
Digital (105, 248, 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
(248−143, 248, 144)-Net over F4 — Digital
Digital (105, 248, 144)-net over F4, using
- t-expansion [i] based on digital (91, 248, 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
(248−143, 248, 1072)-Net in Base 4 — Upper bound on s
There is no (105, 248, 1073)-net in base 4, because
- 1 times m-reduction [i] would yield (105, 247, 1073)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 53595 132513 616550 807705 221921 000566 047767 391638 308386 442425 554885 414589 840397 357476 082414 055826 958460 609266 218657 754249 756720 743593 933914 524558 014720 > 4247 [i]