Best Known (180−111, 180, s)-Nets in Base 4
(180−111, 180, 66)-Net over F4 — Constructive and digital
Digital (69, 180, 66)-net over F4, using
- t-expansion [i] based on digital (49, 180, 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
(180−111, 180, 99)-Net over F4 — Digital
Digital (69, 180, 99)-net over F4, using
- t-expansion [i] based on digital (61, 180, 99)-net over F4, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 61 and N(F) ≥ 99, using
- net from sequence [i] based on digital (61, 98)-sequence over F4, using
(180−111, 180, 603)-Net in Base 4 — Upper bound on s
There is no (69, 180, 604)-net in base 4, because
- 1 times m-reduction [i] would yield (69, 179, 604)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 603475 730032 790098 775151 340611 001573 920370 552591 923531 668587 714818 257410 344564 576503 314170 678098 141598 668164 > 4179 [i]