MinT - Best Known (64−32, 64, s)-Nets in Base 4

Best Known (64−32, 64, s)-Nets in Base 4

Digital (32, 64, 44)-net over F₄, using

(32, 64, 46)-net in base 4, using

2 times m-reduction [i] based on (32, 66, 46)-net in base 4, using
- base change [i] based on digital (10, 44, 46)-net over F₈, using
  - net from sequence [i] based on digital (10, 45)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 9, N(F)Â =Â 45, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]

Digital (32, 64, 60)-net over F₄, using

t-expansion [i] based on digital (31, 64, 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, 64, 568)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 344 224451 789576 870836 976716 153273 097035 > 4⁶⁴ [i]