MinT - Best Known (85, 85+65, s)-Nets in Base 4

Best Known (85, 85+65, s)-Nets in Base 4

(85, 85+65, 130)-Net over F₄ — Constructive and digital

Digital (85, 150, 130)-net over F₄, using

8 times m-reduction [i] based on digital (85, 158, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 79, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(85, 85+65, 176)-Net over F₄ — Digital

Digital (85, 150, 176)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 85+65, 2684)-Net in Base 4 — Upper bound on s

There is no (85, 150, 2685)-net in base 4, because

1 times m-reduction [i] would yield (85, 149, 2685)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 510754 795990 695592 475945 506586 418650 838903 583813 978698 941929 703385 508765 394157 227923 912885 > 4¹⁴⁹ [i]