MinT - Best Known (70−50, 70, s)-Nets in Base 4

Best Known (70−50, 70, s)-Nets in Base 4

(70−50, 70, 33)-Net over F₄ — Constructive and digital

Digital (20, 70, 33)-net over F₄, using

t-expansion [i] based on digital (15, 70, 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]

(70−50, 70, 41)-Net over F₄ — Digital

Digital (20, 70, 41)-net over F₄, using

t-expansion [i] based on digital (18, 70, 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]

(70−50, 70, 105)-Net in Base 4 — Upper bound on s

There is no (20, 70, 106)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁷⁰, 106, S₄, 50), but
- the linear programming bound shows that MÂ â‰¥ 54 896120 505937 298387 270537 967954 682648 627253 567343 802417 950315 257532 514304 / 35 482011 486720 529033 080767 929775 > 4⁷⁰ [i]