MinT - Best Known (31−23, 31, s)-Nets in Base 4

Best Known (31−23, 31, s)-Nets in Base 4

(31−23, 31, 21)-Net over F₄ — Constructive and digital

Digital (8, 31, 21)-net over F₄, using

t-expansion [i] based on digital (7, 31, 21)-net over F₄, using
- net from sequence [i] based on digital (7, 20)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]

(31−23, 31, 59)-Net in Base 4 — Upper bound on s

There is no (8, 31, 60)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4³¹, 60, S₄, 23), but
- the linear programming bound shows that MÂ â‰¥ 475006 970662 079620 526789 858251 797365 798224 857648 683079 581845 946368 / 95021 261803 836035 195255 058030 413106 027157 294057 > 4³¹ [i]