MinT - Best Known (20, 76, s)-Nets in Base 4

Best Known (20, 76, s)-Nets in Base 4

(20, 76, 33)-Net over F₄ — Constructive and digital

Digital (20, 76, 33)-net over F₄, using

t-expansion [i] based on digital (15, 76, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(20, 76, 41)-Net over F₄ — Digital

Digital (20, 76, 41)-net over F₄, using

t-expansion [i] based on digital (18, 76, 41)-net over F₄, using
- net from sequence [i] based on digital (18, 40)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 18 and N(F) ≥ 41, using
    - Drinfeld modules of rank 1 [i]

(20, 76, 90)-Net in Base 4 — Upper bound on s

There is no (20, 76, 91)-net in base 4, because

1 times m-reduction [i] would yield (20, 75, 91)-net in base 4, but
- extracting embedded orthogonal array [i] would yield OA(4⁷⁵, 91, S₄, 55), but
  - the linear programming bound shows that MÂ â‰¥ 28 950790 936281 429398 007109 611762 723777 968090 108196 290560 / 18104 568013 > 4⁷⁵ [i]