MinT - Best Known (65−46, 65, s)-Nets in Base 4

Best Known (65−46, 65, s)-Nets in Base 4

(65−46, 65, 33)-Net over F₄ — Constructive and digital

Digital (19, 65, 33)-net over F₄, using

t-expansion [i] based on digital (15, 65, 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]

(65−46, 65, 41)-Net over F₄ — Digital

Digital (19, 65, 41)-net over F₄, using

t-expansion [i] based on digital (18, 65, 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]

(65−46, 65, 112)-Net in Base 4 — Upper bound on s

There is no (19, 65, 113)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶⁵, 113, S₄, 46), but
- the linear programming bound shows that MÂ â‰¥ 145 402369 805359 268193 209685 952643 209942 587568 332064 303419 732807 154505 932977 868145 129044 024267 389501 535040 862760 730624 / 100423 807776 117676 644806 780906 988983 236254 180840 898357 650546 636091 023031 034405 > 4⁶⁵ [i]