MinT - Best Known (77−45, 77, s)-Nets in Base 4

Best Known (77−45, 77, s)-Nets in Base 4

Digital (32, 77, 35)-net over F₄, using

(32, 77, 43)-net in base 4, using

t-expansion [i] based on (30, 77, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
  - base expansion [i] based on digital (60, 42)-sequence over F₂, using
    - t-expansion [i] based on digital (59, 42)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 54, N(F)Â =Â 42, and 1 place with degree 6 [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]

Digital (32, 77, 60)-net over F₄, using

t-expansion [i] based on digital (31, 77, 60)-net over F₄, using
- net from sequence [i] based on digital (31, 59)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 31 and N(F) ≥ 60, using
    - Drinfeld modules of rank 1 [i]

There is no (32, 77, 346)-net in base 4, because

1 times m-reduction [i] would yield (32, 76, 346)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5985 465730 455817 416538 857957 142172 157961 418236 > 4⁷⁶ [i]