MinT - Best Known (32, 32+77, s)-Nets in Base 4

Best Known (32, 32+77, s)-Nets in Base 4

Digital (32, 109, 34)-net over F₄, using

t-expansion [i] based on digital (21, 109, 34)-net over F₄, using
- net from sequence [i] based on digital (21, 33)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
    - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(32, 109, 43)-net in base 4, using

t-expansion [i] based on (30, 109, 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, 109, 60)-net over F₄, using

t-expansion [i] based on digital (31, 109, 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, 109, 148)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4¹⁰⁹, 148, S₄, 77), but
- the linear programming bound shows that MÂ â‰¥ 93369 878733 386831 807951 664767 066779 195616 328505 480197 805811 746625 475920 186816 273170 627753 565380 149248 / 221551 214490 977896 234087 779488 628125 > 4¹⁰⁹ [i]